Monday, January 20, 2014

Interstellar travel

From Wikipedia, the free encyclopedia

Interstellar space travel is manned or unmanned travel between stars. The concept of interstellar travel via starships is a staple of science fiction. Interstellar travel is conceptually much more difficult than interplanetary travel. The distance between the planets in the Solar System is typically measured in standard astronomical units, while the distance between the stars is hundreds of thousands of AU and often expressed in light years. Intergalactic travel, or travel between different galaxies, would be even more difficult.
A variety of concepts have been discussed in the literature, since the first astronautical pioneers, such as Konstantin Tsiolkovsky, Robert Esnault-Pelterie and Robert Hutchings Goddard. Given sufficient travel time and engineering work, both unmanned and sleeper ship interstellar travel requires no break-through physics to be achieved, but considerable technological and economic challenges need to be met. NASA, ESA and other space agencies have been engaging in research into these topics for decades, and have accumulated a number of theoretical approaches.

Difficulties

The main challenge facing interstellar travel is the immense distances between the stars. This means both great speed and a long travel time are required. The time required by propulsion methods based on currently known physical principles would require years to millennia. Hence an interstellar ship would face manifold hazards found in interplanetary travel, including vacuum, radiation, weightlessness, and micrometeoroids. Even the minimum multi-year travel times to the nearest stars are beyond current manned space mission design experience. The fundamental limits of spacetime present another challenge. The distances between stars isn't a problem in and of itself. Virtually all the material that would pose a problem is in our solar system along the disk that contains the planets, asteroid belt, Oort cloud, comets, free asteroids, macro and micro-meteroids, etc. So any device or projectile must be sent in a direction opposite of all of this material. The larger the object humans send, the greater the chances of it hitting something or vice versa. One option is to project something very small where the chance of it striking or being struck by something is virtually non-existent in the vacuum of interplanetary and interstellar space.^[1]^[2]

Required energy

A significant factor contributing to the difficulty is the energy which must be supplied to obtain a reasonable travel time. A lower bound for the required energy is the kinetic energy K = ½ mv² where m is the final mass. If deceleration on arrival is desired and cannot be achieved by any means other than the engines of the ship, then the required energy at least doubles, because the energy needed to halt the ship equals the energy needed to accelerate it to travel speed.
The velocity for a manned round trip of a few decades to even the nearest star is several thousand times greater than those of present space vehicles. This means that due to the v² term in the kinetic energy formula, millions of times as much energy is required. Accelerating one ton to one-tenth of the speed of light requires at least 450 PJ or 4.5 ×10¹⁷ J or 125 billion kWh, without factoring in efficiency of the propulsion mechanism. This energy has to be either generated on-board from stored fuel, harvested from the interstellar medium, or projected over immense distances.
The energy requirements make interstellar travel very difficult. It has been reported that at the 2008 Joint Propulsion Conference, multiple experts opined that it was improbable that humans would ever explore beyond the Solar System.^[3] Brice N. Cassenti, an associate professor with the Department of Engineering and Science at Rensselaer Polytechnic Institute, stated that at least the total energy output of the entire world [in a given year] would be required to send a probe to the nearest star.^[3]

Interstellar medium

A major issue with traveling at extremely high speeds is that interstellar dust and gas may cause considerable damage to the craft, due to the high relative speeds and large kinetic energies involved. Various shielding methods to mitigate this problem have been proposed.^{[citation needed]} Larger objects (such as macroscopic dust grains) are far less common, but would be much more destructive. The risks of impacting such objects, and methods of mitigating these risks, have been discussed in the literature, but many unknowns remain.^{[citation needed]}

Travel time

It has been argued that an interstellar mission which cannot be completed within 50 years should not be started at all. Instead, assuming that a civilization is still on an increasing curve of propulsion system velocity, not yet having reached the limit, the resources should be invested in designing a better propulsion system. This is because a slow spacecraft would probably be passed by another mission sent later with more advanced propulsion (Incessant Obsolescence Postulate).^[4] On the other hand, Andrew Kennedy has shown that if one calculates the journey time to a given destination as the rate of travel speed derived from growth (even exponential growth) increases, there is a clear minimum in the total time to that destination from now (see wait calculation).^[5] Voyages undertaken before the minimum will be overtaken by those who leave at the minimum, while those who leave after the minimum will never overtake those who left at the minimum.
One argument against the stance of delaying a start until reaching fast propulsion system velocity is that the various other non-technical problems that are specific to long-distance travel at considerably higher speed (such as interstellar particle impact, possible dramatic shortening of average human life span during extended space residence, etc.) may remain obstacles that take much longer time to resolve than the propulsion issue alone, assuming that they can even be solved eventually at all. A case can therefore be made for starting a mission without delay, based on the concept of an achievable and dedicated but relatively slow interstellar mission using the current technological state-of-the-art and at relatively low cost, rather than banking on being able to solve all problems associated with a faster mission without having a reliable time frame for achievability of such.
Intergalactic travel involves distances about a million-fold greater than interstellar distances, making it radically more difficult than even interstellar travel.

Interstellar distances

Astronomical distances are often measured in the time it would take a beam of light to travel between two points (see light-year). Light in a vacuum travels approximately 300,000 kilometers per second or 186,000 miles per second.
The distance from Earth to the Moon is 1.3 light-seconds. With current spacecraft propulsion technologies, a craft can cover the distance from the Earth to the Moon in around eight hours (New Horizons). That means light travels approximately thirty thousand times faster than current spacecraft propulsion technologies. The distance from Earth to other planets in the Solar System ranges from three light-minutes to about four light-hours. Depending on the planet and its alignment to Earth, for a typical unmanned spacecraft these trips will take from a few months to a little over a decade.^{[citation needed]}
The nearest known star to the Sun is Proxima Centauri, which is 4.23 light-years away. However, there may be undiscovered brown dwarf systems that are closer.^[6] The fastest outward-bound spacecraft yet sent, Voyager 1, has covered 1/600th of a light-year in 30 years and is currently moving at 1/18,000th the speed of light. At this rate, a journey to Proxima Centauri would take 80,000 years.^[7] Of course, this mission was not specifically intended to travel fast to the stars, and current technology could do much better. The travel time could be reduced to a millennium using solar sails, or to a century or less using nuclear pulse propulsion. A better understanding of the vastness of the interstellar distance to one of the closest stars to the sun, Alpha Centauri A (a Sun-like star), can be obtained by scaling down the Earth-Sun distance (~150,000,000 km) to one meter. On this scale the distance to Alpha Centauri A would still be 271 kilometers or about 169 miles.
However, more speculative approaches to interstellar travel offer the possibility of circumventing these difficulties. Special relativity offers the possibility of shortening the travel time: if a starship with sufficiently advanced engines could reach velocities approaching the speed of light, relativistic time dilation would make the voyage much shorter for the traveler. However, it would still take many years of elapsed time as viewed by the people remaining on Earth, and upon returning to Earth, the travelers would find that far more time had elapsed on Earth than had for them. (For more on this effect, see twin paradox.)
General relativity offers the theoretical possibility that faster-than-light travel may be possible without violating fundamental laws of physics, for example, through wormholes, although it is still debated whether this is possible, in part, because of causality concerns. Proposed mechanisms for faster-than-light travel within the theory of general relativity require the existence of exotic matter.

Communications

The round-trip delay time is the minimum time between an observation by the probe and the moment the probe can receive instructions from Earth reacting to the observation. Given that information can travel no faster than the speed of light, this is for the Voyager 1 about 17 hours, near Proxima Centauri it would be 8 years. Faster reaction would have to be programmed to be carried out automatically. Of course, in the case of a manned flight the crew can respond immediately to their observations. However, the round-trip delay time makes them not only extremely distant from, but, in terms of communication, also extremely isolated from Earth (analogous to how past long distance explorers were similarly isolated before the invention of the electrical telegraph).
Interstellar communication is still problematic — even if a probe could reach the nearest star, its ability to communicate back to Earth would be difficult given the extreme distance. See Interstellar communication.

Prime targets for interstellar travel

There are 59 known stellar systems within 20 light years from the Sun, containing 81 visible stars.

Manned missions

The mass of any craft capable of carrying humans would inevitably be substantially larger than that necessary for an unmanned interstellar probe. For instance, the first space probe, Sputnik 1, had a payload of 83.6 kg, while spacecraft to carry a living passenger (Laika the dog), Sputnik 2, had a payload six times that at 508.3 kg. This underestimates the difference in the case of interstellar missions, given the vastly greater travel times involved and the resulting necessity of a closed-cycle life support system. As technology continues to advance, combined with the aggregate risks and support requirements of manned interstellar travel, the first interstellar missions are unlikely to carry earthly life forms.
A manned craft will require more time to reach its top speed as humans have limited tolerance to acceleration.

Time dilation

Main article: Time dilation

Assuming one can not travel faster than light, one might conclude that a human can never make a round-trip further from the Earth than 40 light years if the traveler is active between the ages of 20 and 60. So a traveler would never be able to reach more than the very few star systems which exist within the limit of 10–20 light years from the Earth.
But that would be a mistaken conclusion because it fails to take into account time dilation. Informally explained, clocks aboard ship run slower than Earth clocks, so if the ship engines are powerful enough the ship can reach mostly anywhere in the galaxy and go back to Earth within 40 years ship-time. The problem is that there is a difference between the time elapsed in the astronaut's ship and the time elapsed on Earth.
An example will make this clearer. Suppose a spaceship travels to a star 32 light years away. First it accelerates at a constant 1.03g (i.e., 10.1 m/s²) for 1.32 years (ship time). Then it stops the engines and coasts for the next 17.3 years (ship time) at a constant speed. Then it decelerates again for 1.32 ship-years so as to come at a stop at the destination. The astronaut takes a look around and comes back to Earth the same way.
After the full round-trip, the clocks on board the ship show that 40 years have passed, but according to Earth calendar the ship comes back 76 years after launch.
So, the overall average speed is 0.84 lightyears per earth year, or 1.6 lightyears per ship year. This is possible because at a speed of 0.87 c, time on board the ship seems to run slower. Every two Earth years, ship clocks advance 1 year.
From the viewpoint of the astronaut, onboard clocks seem to be running normally. The star ahead seems to be approaching at a speed of 0.87 lightyears per ship year. As all the universe looks contracted along the direction of travel to half the size it had when the ship was at rest, the distance between that star and the Sun seems to be 16 light years as measured by the astronaut, so it's no wonder that the trip at 0.87 ly per shipyear takes 20 ship years.
At higher speeds, the time onboard will run even slower, so the astronaut could travel to the center of the Milky Way (30 kly from Earth) and back in 40 years ship-time. But the speed according to Earth clocks will always be less than 1 lightyear per Earth year, so, when back home, the astronaut will find that 60 thousand years will have passed on Earth.

Constant acceleration

Regardless of how it is achieved, if a propulsion system can produce 1 g of acceleration continuously from departure to destination, then this will be the fastest method of travel. If the propulsion system drives the ship faster and faster for the first half of the journey, then turns around and brakes the craft so that it arrives at the destination at a standstill, this is a constant acceleration journey. This would also have the advantage of producing constant gravity.
From the planetary observer perspective the ship will appear to steadily accelerate but more slowly as it approaches the speed of light. The ship will be close to the speed of light after about a year of accelerating and remain at that speed until it brakes for the end of the journey.
From the ship perspective there will be no top limit on speed – the ship keeps going faster and faster the whole first half. This happens because the ship's time sense slows down – relative to the planetary observer – the more it approaches the speed of light.
The result is an impressively fast journey if you are in the ship. Here is a table of journey times, in years, for various constant accelerations.

Destination	1g	2g	5g	10g	Planetary time frame (all in years)
Alpha Centauri	4	2.8	1.8	1.3	5
Sirius	7	5	3	2.2	13
Galactic Core	340	244	155	110	30,000

Note again, that times observed from the planetary frame of reference (which applies to both departure and destination points) are very different from those observed in the space craft, and that from the ship frame of reference there is no limit on the top speed.^[13]

Proposed methods

Slow manned missions

Potential slow manned interstellar travel missions, based on current and near-future propulsion technologies are associated with trip times, starting from about one hundred years to thousands of years. The duration of a slow interstellar journey presents a major obstacle and existing concepts deal with this problem in different ways.^[14] They can be distinguished by the "state" in which humans are transported on-board of the spacecraft.

Generation ships

Main article: Generation ship

A generation ship (or world ship) is a type of interstellar ark in which the crew which arrives at the destination is descended from those who started the journey. Generation ships are not currently feasible because of the difficulty of constructing a ship of the enormous required scale and the great biological and sociological problems that life aboard such a ship raises.^[15]^[16]^[17]^[18]

Suspended animation

Scientists and writers have postulated various techniques for suspended animation. These include human hibernation and cryonic preservation. While neither is currently practical, they offer the possibility of sleeper ships in which the passengers lie inert for the long years of the voyage.^[19]

Extended human lifespan

A variant on this possibility is based on the development of substantial human life extension, such as the "Strategies for Engineered Negligible Senescence" proposed by Dr. Aubrey de Grey. If a ship crew had lifespans of some thousands of years, or had artificial bodies, they could traverse interstellar distances without the need to replace the crew in generations. The psychological effects of such an extended period of travel would potentially still pose a problem.

Frozen embryos

Main article: Embryo space colonization

A robotic space mission carrying some number of frozen early stage human embryos is another theoretical possibility. This method of space colonization requires, among other things, the development of a method to replicate conditions in a uterus, the prior detection of a habitable terrestrial planet, and advances in the field of fully autonomous mobile robots and educational robots which would replace human parents.^[20]

Island hopping through interstellar space

Interstellar space is not completely empty; it contains trillions of icy bodies ranging from small asteroids (Oort cloud) to possible rogue planets. There may be ways to take advantage of these resources for a good part of an interstellar trip, slowly hopping from body to body or setting up waystations along the way.^[21]

Faster manned missions

If a spaceship could average 10 percent of light speed (and decelerate at the destination, for manned missions), this would be enough to reach Proxima Centauri in forty years. Several propulsion concepts are proposed that might be eventually developed to accomplish this (see section below on propulsion methods), but none of them are ready for near-term (few decades) development at acceptable cost.^{[citation needed]}

Unmanned

Nanoprobes

Near-lightspeed nanospacecraft might be possible within the near future built on existing microchip technology with a newly developed nanoscale thruster. Researchers at the University of Michigan are developing thrusters that use nanoparticles as propellant. Their technology is called “nanoparticle field extraction thruster”, or nanoFET. These devices act like small particle accelerators shooting conductive nanoparticles out into space.^[22]
Given the light weight of these probes, it would take much less energy to accelerate them. With on board solar cells they could continually accelerate using solar power. One can envision a day when a fleet of millions or even billions of these particles swarm to distant stars at nearly the speed of light, while relaying signals back to earth through a vast interstellar communication network.

Ships with an external energy source

There are projects ships supplying energy from external sources such as using laser. Thus reduced mass of the ship due to the lack of energy system on board the ship that makes it easier and allows us to develop more speed. Geoffrey A. Landis proposed for interstellar travel future-technology project interstellar probe with supplying the energy from an external source (laser of base station) and Ion thruster.^[23]^[24]^[25]^[26]

Propulsion

Rocket concepts

All rocket concepts are limited by the rocket equation, which sets the characteristic velocity available as a function of exhaust velocity and mass ratio, the ratio of initial (M₀, including fuel) to final (M₁, fuel depleted) mass.
Very high specific power, the ratio of jet-power to total vehicle mass, is required to reach interstellar targets within sub-century time-frames.^[27] Some heat transfer is inevitable and a tremendous heating load must be adequately handled.
Thus, for interstellar rocket concepts of all technologies, a key engineering problem (seldom explicitly discussed) is limiting the heat transfer from the exhaust stream back into the vehicle.^[28]

Nuclear fission powered

Fission-electric

Nuclear-electric or plasma engines, operating for long periods at low thrust and powered by fission reactors, have the potential to reach speeds much greater than chemically powered vehicles or nuclear-thermal rockets. Such vehicles probably have the potential to power Solar System exploration with reasonable trip times within the current century. Because of their low-thrust propulsion, they would be limited to off-planet, deep-space operation. Electrically powered spacecraft propulsion powered by a portable power-source, say a nuclear reactor, producing only small cravings, a lot of weight needed to convert nuclear energy into electrical equipment and as a consequence low accelerations, would take centuries to reach for example 15% of the velocity of light, thus unsuitable for interstellar flight in during a one human lifetime.^[29]^[30]^[31]

Fission-fragment

Fission-fragment rockets use nuclear fission to create high-speed jets of fission fragments, which are ejected at speeds of up to 12,000 km/s. With fission, the energy output is approximately 0.1% of the total mass-energy of the reactor fuel and limits the effective exhaust velocity to about 5% of the velocity of light. For maximum velocity, the reaction mass should optimally consist of fission products, the "ash" of the primary energy source, in order that no extra reaction mass need be book-kept in the mass ratio. This is known as a fission-fragment rocket. thermal-propulsion engines such as NERVA produce sufficient thrust, but can only achieve relatively low-velocity exhaust jets, so to accelerate to the desired speed would require an enormous amount of fuel.^[29]^[30]^[31]

Nuclear pulse

Main article: Nuclear pulse propulsion

Based on work in the late 1950s to the early 1960s, it has been technically possible to build spaceships with nuclear pulse propulsion engines, i.e. driven by a series of nuclear explosions. This propulsion system contains the prospect of very high specific impulse (space travel's equivalent of fuel economy) and high specific power.^[32]
Project Orion team member, Freeman Dyson, proposed in 1968 an interstellar spacecraft using nuclear pulse propulsion which used pure deuterium fusion detonations with a very high fuel-burnup fraction. He computed an exhaust velocity of 15,000 km/s and a 100,000 tonne space-vehicle able to achieve a 20,000 km/s delta-v allowing a flight-time to Alpha Centauri of 130 years.^[33] Later studies indicate that the top cruise velocity that can theoretically be achieved by a Teller-Ulam thermonuclear unit powered Orion starship, assuming no fuel is saved for slowing back down, is about 8% to 10% of the speed of light (0.08-0.1c).^[34] An atomic (fission) Orion can achieve perhaps 3%-5% of the speed of light. A nuclear pulse drive starship powered by Fusion-antimatter catalyzed nuclear pulse propulsion units would be similarly in the 10% range and pure Matter-antimatter annihilation rockets would be theoretically capable of obtaining a velocity between 50% to 80% of the speed of light. In each case saving fuel for slowing down halves the max. speed. The concept of using a magnetic sail to decelerate the spacecraft as it approaches its destination has been discussed as an alternative to using propellant, this would allow the ship to travel near the maximum theoretical velocity.^[35] Alternative designs utilizing similar principles include Project Longshot, Project Daedalus, and Mini-Mag Orion. The principle of external nuclear pulse propulsion to maximize survivable power has remained common among serious concepts for interstellar flight without external power beaming and for very high-performance interplanetary flight.
In the 1970s the Nuclear Pulse Propulsion concept further was refined by Project Daedalus by use of externally triggered inertial confinement fusion, in this case producing fusion explosions via compressing fusion fuel pellets with high-powered electron beams. Since then lasers, ion beams, neutral particle beams and hyper-kinetic projectiles have been suggested to produce nuclear pulses for propulsion purposes.^[36]
A current impediment to the development of any nuclear explosive powered spacecraft is the 1963 Partial Test Ban Treaty which includes a prohibition on the detonation of any nuclear devices (even non-weapon based) in outer space. This treaty would therefore need to be re-negotiated, although a project on the scale of an interstellar mission using currently foreseeable technology would probably require international co-operation on at least the scale of the International Space Station.

Nuclear fusion rockets

Fusion rocket starships, powered by nuclear fusion reactions, should conceivably be able to reach speeds of the order of 10% of that of light, based on energy considerations alone. In theory, a large number of stages could push a vehicle arbitrarily close to the speed of light.^[37] These would "burn" such light element fuels as deuterium, tritium, ³He, ¹¹B, and ⁷Li. Because fusion yields about 0.3–0.9% of the mass of the nuclear fuel as released energy, it is energetically more favorable than fission, which releases <0.1% of the fuel's mass-energy. The maximum exhaust velocities potentially energetically available are correspondingly higher than for fission, typically 4–10% of c. However, the most easily achievable fusion reactions release a large fraction of their energy as high-energy neutrons, which are a significant source of energy loss. Thus, while these concepts seem to offer the best (nearest-term) prospects for travel to the nearest stars within a (long) human lifetime, they still involve massive technological and engineering difficulties, which may turn out to be intractable for decades or centuries.
Early studies include Project Daedalus, performed by the British Interplanetary Society in 1973–1978, and Project Longshot, a student project sponsored by NASA and the US Naval Academy, completed in 1988. Another fairly detailed vehicle system, "Discovery II",^[38] designed and optimized for crewed Solar System exploration, based on the D³He reaction but using hydrogen as reaction mass, has been described by a team from NASA's Glenn Research Center. It achieves characteristic velocities of >300 km/s with an acceleration of ~1.7•10⁻³ g, with a ship initial mass of ~1700 metric tons, and payload fraction above 10%. While these are still far short of the requirements for interstellar travel on human timescales, the study seems to represent a reasonable benchmark towards what may be approachable within several decades, which is not impossibly beyond the current state-of-the-art. Based on the concept's 2.2% burnup fraction it could achieve a pure fusion product exhaust velocity of ~3,000 km/s.

Antimatter rockets

An antimatter rocket would have a far higher energy density and specific impulse than any other proposed class of rocket. If energy resources and efficient production methods are found to make antimatter in the quantities required and store it safely, it would be theoretically possible to reach speeds approaching that of light. Then relativistic time dilation would become more noticeable, thus making time pass at a slower rate for the travelers as perceived by an outside observer, reducing the trip time experienced by human travelers.
Supposing the production and storage of antimatter should become practical, two further problems would present and need to be solved. First, in the annihilation of antimatter, much of the energy is lost in very penetrating high-energy gamma radiation, and especially also in neutrinos, so that substantially less than mc² would actually be available if the antimatter were simply allowed to annihilate into radiations thermally. Even so, the energy available for propulsion would probably be substantially higher than the ~1% of mc² yield of nuclear fusion, the next-best rival candidate.
Second, once again heat transfer from exhaust to vehicle seems likely to deposit enormous wasted energy into the ship, considering the large fraction of the energy that goes into penetrating gamma rays. Even assuming biological shielding were provided to protect the passengers, some of the energy would inevitably heat the vehicle, and may thereby prove limiting. This requires consideration for serious proposals if useful accelerations are to be achieved, as the energies involved (e.g., for 0.1g ship acceleration, approaching 0.3 trillion watts per ton of ship mass) are very large.
Recently Friedwardt Winterberg has suggested a means of converting an imploding matter-antimatter plasma into a highly collimated beam of gamma-rays - effectively a gamma-ray laser - which would very efficiently transfer thrust to the space vehicle's structure via a variant of the Mössbauer effect.^[39] Such a system, if antimatter production can be made efficient, would then be a very effective photon rocket, as originally envisaged by Eugen Sanger.
^[40]

Non-rocket concepts

A problem with all traditional rocket propulsion methods is that the spacecraft would need to carry its fuel with it, thus making it very massive, in accordance with the rocket equation. Some concepts attempt to escape from this problem (^[41]):

Interstellar ramjets

In 1960, Robert W. Bussard proposed the Bussard ramjet, a fusion rocket in which a huge scoop would collect the diffuse hydrogen in interstellar space, "burn" it on the fly using a proton–proton fusion reaction, and expel it out of the back. Though later calculations with more accurate estimates suggest that the thrust generated would be less than the drag caused by any conceivable scoop design, the idea is attractive because, as the fuel would be collected en route (commensurate with the concept of energy harvesting), the craft could theoretically accelerate to near the speed of light.

Beamed propulsion

This diagram illustrates Robert L. Forward's scheme for slowing down an interstellar light-sail at the destination ^[42] system.

A light sail or magnetic sail powered by a massive laser or particle accelerator in the home star system could potentially reach even greater speeds than rocket- or pulse propulsion methods, because it would not need to carry its own reaction mass and therefore would only need to accelerate the craft's payload. Robert L. Forward proposed a means for decelerating an interstellar light sail in the destination star system without requiring a laser array to be present in that system. In this scheme, a smaller secondary sail is deployed to the rear of the spacecraft, while the large primary sail is detached from the craft to keep moving forward on its own. Light is reflected from the large primary sail to the secondary sail, which is used to decelerate the secondary sail and the spacecraft payload.^[43]
A magnetic sail could also decelerate at its destination without depending on carried fuel or a driving beam in the destination system, by interacting with the plasma found in the solar wind of the destination star and the interstellar medium.^[44] Unlike Forward's light sail scheme, this would not require the action of the particle beam used for launching the craft. Alternatively, a magnetic sail could be pushed by a particle beam^[45] or a plasma beam^[46] to reach high velocity, as proposed by Landis and Winglee.
Beamed propulsion seems to be the best interstellar travel technique presently available, since it uses known physics and known technology that is being developed for other purposes,^[8] and would be considerably cheaper than nuclear pulse propulsion.^{[citation needed]}

Pre-accelerated fuel

Achieving start-stop interstellar trip times of less than a human lifetime require mass-ratios of between 1,000 and 1,000,000, even for the nearer stars. This could be achieved by multi-staged vehicles on a vast scale.^[37] Alternatively large linear accelerators could propel fuel to fission propelled space-vehicles, avoiding the limitations of the Rocket equation.^[48]

Speculative methods

Hawking radiation rockets

In a black hole starship, a parabolic reflector would reflect Hawking radiation from an artificial black hole. In 2009, Louis Crane and Shawn Westmoreland of Kansas State University published a paper investigating the feasibility of this idea. Their conclusion was that it was on the edge of possibility, but that quantum gravity effects that are presently unknown may make it easier or make it impossible.^[49]^[50]

Magnetic monopole rockets

If some of the Grand unification models are correct, e.g. 't Hooft–Polyakov, it would be possible to construct a photonic engine that uses no antimatter thanks to the magnetic monopole which hypothetically can catalyze decay of a proton to a positron and π⁰-meson:^[51]^[52]

$p \rarr e^{+} + \pi^0$

π⁰ decays rapidly to two photons, and the positron annihilates with an electron to give two more photons. As a result, a hydrogen atom turns into four photons and only the problem of a mirror remains unresolved.
A magnetic monopole engine could also work on a once-through scheme such as the Bussard ramjet (see below).
At the same time, most of the modern Grand unification theories such as M-theory predict no magnetic monopoles, which casts doubt on this attractive idea.

By transmission

Main article: Teleportation

If physical entities could be transmitted as information and reconstructed at a destination, travel at nearly the speed of light would be possible, which for the "travelers" would be instantaneous. However, sending an atom-by-atom description of (say) a human body would be a daunting task. Extracting and sending only a computer brain simulation is a significant part of that problem. "Journey" time would be the light-travel time plus the time needed to encode, send and reconstruct the whole transmission.^[53]

Faster-than-light travel

Artist's depiction of a hypothetical Wormhole Induction Propelled Spacecraft, based loosely on the 1994 "warp drive" paper of Miguel Alcubierre. Credit: NASA CD-98-76634 by Les Bossinas.

Main article: Faster-than-light

Scientists and authors have postulated a number of ways by which it might be possible to surpass the speed of light. Even the most serious-minded of these are speculative.
According to Einstein's equation of general relativity, spacetime is curved:

$G_{\mu\nu}=8\pi\,GT_{\mu\nu} \,$

General relativity may permit the travel of an object faster than light in curved spacetime.^[54] One could imagine exploiting the curvature to take a "shortcut" from one point to another. This is one form of the warp drive concept.
In physics, the Alcubierre drive is based on an argument that the curvature could take the form of a wave in which a spaceship might be carried in a "bubble". Space would be collapsing at one end of the bubble and expanding at the other end. The motion of the wave would carry a spaceship from one space point to another in less time than light would take through unwarped space. Nevertheless, the spaceship would not be moving faster than light within the bubble. This concept would require the spaceship to incorporate a region of exotic matter, or "negative mass".
Wormholes are conjectural distortions in spacetime that theorists postulate could connect two arbitrary points in the universe, across an Einstein–Rosen Bridge. It is not known whether wormholes are possible in practice. Although there are solutions to the Einstein equation of general relativity which allow for wormholes, all of the currently known solutions involve some assumption, for example the existence of negative mass, which may be unphysical.^[55] However, Cramer et al. argue that such wormholes might have been created in the early universe, stabilized by cosmic string.^[56] The general theory of wormholes is discussed by Visser in the book Lorentzian Wormholes.^[57]

Designs and studies

Project Hyperion

Project Hyperion, one of the projects of Icarus Interstellar.^[58]

Enzmann starship

Main article: Enzmann starship

The Enzmann starship, as detailed by G. Harry Stine in the October 1973 issue of Analog, was a design for a future starship, based on the ideas of Dr. Robert Duncan-Enzmann.^[59] The spacecraft itself as proposed used a 12,000,000 ton ball of frozen deuterium to power 12–24 thermonuclear pulse propulsion units.^[59] Twice as long as the Empire State Building and assembled in-orbit, the spacecraft was part of a larger project preceded by interstellar probes and telescopic observation of target star systems.^[59]^[60]

NASA research

NASA has been researching interstellar travel since its formation, translating important foreign language papers and conducting early studies on applying fusion propulsion, in the 1960s, and laser propulsion, in the 1970s, to interstellar travel.
The NASA Breakthrough Propulsion Physics Program (terminated in FY 2003 after 6-year, $1.2 million study, as "No breakthroughs appear imminent.")^[61] identified some breakthroughs which are needed for interstellar travel to be possible.^[62]
Geoffrey A. Landis of NASA's Glenn Research Center states that a laser-powered interstellar sail ship could possibly be launched within 50 years, using new methods of space travel. "I think that ultimately we're going to do it, it's just a question of when and who," Landis said in an interview. Rockets are too slow to send humans on interstellar missions. Instead, he envisions interstellar craft with extensive sails, propelled by laser light to about one-tenth the speed of light. It would take such a ship about 43 years to reach Alpha Centauri, if it passed through the system. Slowing down to stop at Alpha Centauri could increase the trip to 100 years,^[63] while a journey without slowing down raises the issue of making sufficiently accurate and useful observations and measurements during a fly-by.

Hundred-Year Starship study

The 100 Year Starship (100YSS) is the name of the overall effort that will, over the next century, work toward achieving interstellar travel. The effort will also go by the moniker 100YSS. The 100 Year Starship study is the name of a one year project to assess the attributes of and lay the groundwork for an organization that can carry forward the 100 Year Starship vision.
Dr. Harold ("Sonny") White^[64] from NASA's Johnson Space Center is a member of Icarus Interstellar,^[65] the nonprofit foundation whose mission is to realize interstellar flight before the year 2100. At the 2012 meeting of 100YSS, he reported using a laser to try to warp spacetime by 1 part in 10 million with the aim of helping to make interstellar travel possible.^[66]

General relativity

From Wikipedia, the free encyclopedia

For a more accessible and less technical introduction to this topic, see Introduction to general relativity.

For the book by Robert Wald, see General Relativity (book)

G_{\mu \nu} + \Lambda g_{\mu \nu}= {8\pi G\over c^4} T_{\mu \nu}

A simulated black hole of 10 solar masses as seen from a distance of 600 kilometers with the Milky Way in the background.

General relativity, or the general theory of relativity, is the geometric theory of gravitation published by Albert Einstein in 1915^[1] and the current description of gravitation in modern physics. General relativity generalizes special relativity and Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or spacetime. In particular, the curvature of spacetime is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of partial differential equations.
Some predictions of general relativity differ significantly from those of classical physics, especially concerning the passage of time, the geometry of space, the motion of bodies in free fall, and the propagation of light. Examples of such differences include gravitational time dilation, gravitational lensing, the gravitational redshift of light, and the gravitational time delay. The predictions of general relativity have been confirmed in all observations and experiments to date. Although general relativity is not the only relativistic theory of gravity, it is the simplest theory that is consistent with experimental data. However, unanswered questions remain, the most fundamental being how general relativity can be reconciled with the laws of quantum physics to produce a complete and self-consistent theory of quantum gravity.
Einstein's theory has important astrophysical implications. For example, it implies the existence of black holes—regions of space in which space and time are distorted in such a way that nothing, not even light, can escape—as an end-state for massive stars. There is ample evidence that the intense radiation emitted by certain kinds of astronomical objects is due to black holes; for example, microquasars and active galactic nuclei result from the presence of stellar black holes and black holes of a much more massive type, respectively. The bending of light by gravity can lead to the phenomenon of gravitational lensing, in which multiple images of the same distant astronomical object are visible in the sky. General relativity also predicts the existence of gravitational waves, which have since been observed indirectly; a direct measurement is the aim of projects such as LIGO and NASA/ESA Laser Interferometer Space Antenna and various pulsar timing arrays. In addition, general relativity is the basis of current cosmological models of a consistently expanding universe.

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History[edit]

Main articles: History of general relativity and Classical theories of gravitation

Albert Einstein developed the theories of special and general relativity. Picture from 1921.

Soon after publishing the special theory of relativity in 1905, Einstein started thinking about how to incorporate gravity into his new relativistic framework. In 1907, beginning with a simple thought experiment involving an observer in free fall, he embarked on what would be an eight-year search for a relativistic theory of gravity. After numerous detours and false starts, his work culminated in the presentation to the Prussian Academy of Science in November 1915 of what are now known as the Einstein field equations. These equations specify how the geometry of space and time is influenced by whatever matter and radiation are present, and form the core of Einstein's general theory of relativity.^[2]
The Einstein field equations are nonlinear and very difficult to solve. Einstein used approximation methods in working out initial predictions of the theory. But as early as 1916, the astrophysicist Karl Schwarzschild found the first non-trivial exact solution to the Einstein field equations, the so-called Schwarzschild metric. This solution laid the groundwork for the description of the final stages of gravitational collapse, and the objects known today as black holes. In the same year, the first steps towards generalizing Schwarzschild's solution to electrically charged objects were taken, which eventually resulted in the Reissner–Nordström solution, now associated with electrically charged black holes.^[3] In 1917, Einstein applied his theory to the universe as a whole, initiating the field of relativistic cosmology. In line with contemporary thinking, he assumed a static universe, adding a new parameter to his original field equations—the cosmological constant—to match that observational presumption.^[4] By 1929, however, the work of Hubble and others had shown that our universe is expanding. This is readily described by the expanding cosmological solutions found by Friedmann in 1922, which do not require a cosmological constant. Lemaître used these solutions to formulate the earliest version of the Big Bang models, in which our universe has evolved from an extremely hot and dense earlier state.^[5] Einstein later declared the cosmological constant the biggest blunder of his life.^[6]
During that period, general relativity remained something of a curiosity among physical theories. It was clearly superior to Newtonian gravity, being consistent with special relativity and accounting for several effects unexplained by the Newtonian theory. Einstein himself had shown in 1915 how his theory explained the anomalous perihelion advance of the planet Mercury without any arbitrary parameters ("fudge factors").^[7] Similarly, a 1919 expedition led by Eddington confirmed general relativity's prediction for the deflection of starlight by the Sun during the total solar eclipse of May 29, 1919,^[8] making Einstein instantly famous.^[9] Yet the theory entered the mainstream of theoretical physics and astrophysics only with the developments between approximately 1960 and 1975, now known as the golden age of general relativity.^[10] Physicists began to understand the concept of a black hole, and to identify quasars as one of these objects' astrophysical manifestations.^[11] Ever more precise solar system tests confirmed the theory's predictive power,^[12] and relativistic cosmology, too, became amenable to direct observational tests.^[13]

From classical mechanics to general relativity[edit]

General relativity can be understood by examining its similarities with and departures from classical physics. The first step is the realization that classical mechanics and Newton's law of gravity admit a geometric description. The combination of this description with the laws of special relativity results in a heuristic derivation of general relativity.^[14]

Geometry of Newtonian gravity[edit]

According to general relativity, objects in a gravitational field behave similarly to objects within an accelerating enclosure. For example, an observer will see a ball fall the same way in a rocket (left) as it does on Earth (right), provided that the acceleration of the rocket is equal to 9.8 m/s² (the acceleration due to gravity at the surface of the Earth).

At the base of classical mechanics is the notion that a body's motion can be described as a combination of free (or inertial) motion, and deviations from this free motion. Such deviations are caused by external forces acting on a body in accordance with Newton's second law of motion, which states that the net force acting on a body is equal to that body's (inertial) mass multiplied by its acceleration.^[15] The preferred inertial motions are related to the geometry of space and time: in the standard reference frames of classical mechanics, objects in free motion move along straight lines at constant speed. In modern parlance, their paths are geodesics, straight world lines in curved spacetime.^[16]
Conversely, one might expect that inertial motions, once identified by observing the actual motions of bodies and making allowances for the external forces (such as electromagnetism or friction), can be used to define the geometry of space, as well as a time coordinate. However, there is an ambiguity once gravity comes into play. According to Newton's law of gravity, and independently verified by experiments such as that of Eötvös and its successors (see Eötvös experiment), there is a universality of free fall (also known as the weak equivalence principle, or the universal equality of inertial and passive-gravitational mass): the trajectory of a test body in free fall depends only on its position and initial speed, but not on any of its material properties.^[17] A simplified version of this is embodied in Einstein's elevator experiment, illustrated in the figure on the right: for an observer in a small enclosed room, it is impossible to decide, by mapping the trajectory of bodies such as a dropped ball, whether the room is at rest in a gravitational field, or in free space aboard an accelerating rocket generating a force equal to gravity.^[18]
Given the universality of free fall, there is no observable distinction between inertial motion and motion under the influence of the gravitational force. This suggests the definition of a new class of inertial motion, namely that of objects in free fall under the influence of gravity. This new class of preferred motions, too, defines a geometry of space and time—in mathematical terms, it is the geodesic motion associated with a specific connection which depends on the gradient of the gravitational potential. Space, in this construction, still has the ordinary Euclidean geometry. However, spacetime as a whole is more complicated. As can be shown using simple thought experiments following the free-fall trajectories of different test particles, the result of transporting spacetime vectors that can denote a particle's velocity (time-like vectors) will vary with the particle's trajectory; mathematically speaking, the Newtonian connection is not integrable. From this, one can deduce that spacetime is curved. The result is a geometric formulation of Newtonian gravity using only covariant concepts, i.e. a description which is valid in any desired coordinate system.^[19] In this geometric description, tidal effects—the relative acceleration of bodies in free fall—are related to the derivative of the connection, showing how the modified geometry is caused by the presence of mass.^[20]

Relativistic generalization[edit]

Light cone

As intriguing as geometric Newtonian gravity may be, its basis, classical mechanics, is merely a limiting case of (special) relativistic mechanics.^[21] In the language of symmetry: where gravity can be neglected, physics is Lorentz invariant as in special relativity rather than Galilei invariant as in classical mechanics. (The defining symmetry of special relativity is the Poincaré group which also includes translations and rotations.) The differences between the two become significant when we are dealing with speeds approaching the speed of light, and with high-energy phenomena.^[22]
With Lorentz symmetry, additional structures come into play. They are defined by the set of light cones (see the image on the left). The light-cones define a causal structure: for each event A, there is a set of events that can, in principle, either influence or be influenced by A via signals or interactions that do not need to travel faster than light (such as event B in the image), and a set of events for which such an influence is impossible (such as event C in the image). These sets are observer-independent.^[23] In conjunction with the world-lines of freely falling particles, the light-cones can be used to reconstruct the space–time's semi-Riemannian metric, at least up to a positive scalar factor. In mathematical terms, this defines a conformal structure.^[24]
Special relativity is defined in the absence of gravity, so for practical applications, it is a suitable model whenever gravity can be neglected. Bringing gravity into play, and assuming the universality of free fall, an analogous reasoning as in the previous section applies: there are no global inertial frames. Instead there are approximate inertial frames moving alongside freely falling particles. Translated into the language of spacetime: the straight time-like lines that define a gravity-free inertial frame are deformed to lines that are curved relative to each other, suggesting that the inclusion of gravity necessitates a change in spacetime geometry.^[25]
A priori, it is not clear whether the new local frames in free fall coincide with the reference frames in which the laws of special relativity hold—that theory is based on the propagation of light, and thus on electromagnetism, which could have a different set of preferred frames. But using different assumptions about the special-relativistic frames (such as their being earth-fixed, or in free fall), one can derive different predictions for the gravitational redshift, that is, the way in which the frequency of light shifts as the light propagates through a gravitational field (cf. below). The actual measurements show that free-falling frames are the ones in which light propagates as it does in special relativity.^[26] The generalization of this statement, namely that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames, is known as the Einstein equivalence principle, a crucial guiding principle for generalizing special-relativistic physics to include gravity.^[27]
The same experimental data shows that time as measured by clocks in a gravitational field—proper time, to give the technical term—does not follow the rules of special relativity. In the language of spacetime geometry, it is not measured by the Minkowski metric. As in the Newtonian case, this is suggestive of a more general geometry. At small scales, all reference frames that are in free fall are equivalent, and approximately Minkowskian. Consequently, we are now dealing with a curved generalization of Minkowski space. The metric tensor that defines the geometry—in particular, how lengths and angles are measured—is not the Minkowski metric of special relativity, it is a generalization known as a semi- or pseudo-Riemannian metric. Furthermore, each Riemannian metric is naturally associated with one particular kind of connection, the Levi-Civita connection, and this is, in fact, the connection that satisfies the equivalence principle and makes space locally Minkowskian (that is, in suitable locally inertial coordinates, the metric is Minkowskian, and its first partial derivatives and the connection coefficients vanish).^[28]

Einstein's equations[edit]

Main articles: Einstein field equations and Mathematics of general relativity

Having formulated the relativistic, geometric version of the effects of gravity, the question of gravity's source remains. In Newtonian gravity, the source is mass. In special relativity, mass turns out to be part of a more general quantity called the energy–momentum tensor, which includes both energy and momentum densities as well as stress (that is, pressure and shear).^[29] Using the equivalence principle, this tensor is readily generalized to curved space-time. Drawing further upon the analogy with geometric Newtonian gravity, it is natural to assume that the field equation for gravity relates this tensor and the Ricci tensor, which describes a particular class of tidal effects: the change in volume for a small cloud of test particles that are initially at rest, and then fall freely. In special relativity, conservation of energy–momentum corresponds to the statement that the energy–momentum tensor is divergence-free. This formula, too, is readily generalized to curved spacetime by replacing partial derivatives with their curved-manifold counterparts, covariant derivatives studied in differential geometry. With this additional condition—the covariant divergence of the energy–momentum tensor, and hence of whatever is on the other side of the equation, is zero— the simplest set of equations are what are called Einstein's (field) equations:

Einstein's field equations

G_{\mu\nu}\equiv R_{\mu\nu} - {\textstyle 1 \over 2}R\,g_{\mu\nu} = {8 \pi G \over c^4} T_{\mu\nu}\,

On the left-hand side is the Einstein tensor, a specific divergence-free combination of the Ricci tensor

R_{\mu\nu}

and the metric. Where

G_{\mu\nu}

is symmetric. In particular,

R=g^{\mu\nu}R_{\mu\nu}\,

is the curvature scalar. The Ricci tensor itself is related to the more general Riemann curvature tensor as

R_{\mu\nu}={R^\alpha}_{\mu\alpha\nu}.\,

On the right-hand side, $T_{\mu\nu}$ is the energy–momentum tensor. All tensors are written in abstract index notation.^[30] Matching the theory's prediction to observational results for planetary orbits (or, equivalently, assuring that the weak-gravity, low-speed limit is Newtonian mechanics), the proportionality constant can be fixed as κ = 8πG/c⁴, with G the gravitational constant and c the speed of light.^[31] When there is no matter present, so that the energy–momentum tensor vanishes, the results are the vacuum Einstein equations,

R_{\mu\nu}=0.\,

There are alternatives to general relativity built upon the same premises, which include additional rules and/or constraints, leading to different field equations. Examples are Brans–Dicke theory, teleparallelism, and Einstein–Cartan theory.^[32]

Definition and basic applications[edit]

The derivation outlined in the previous section contains all the information needed to define general relativity, describe its key properties, and address a question of crucial importance in physics, namely how the theory can be used for model-building.

Definition and basic properties[edit]

General relativity is a metric theory of gravitation. At its core are Einstein's equations, which describe the relation between the geometry of a four-dimensional, pseudo-Riemannian manifold representing spacetime, and the energy–momentum contained in that spacetime.^[33] Phenomena that in classical mechanics are ascribed to the action of the force of gravity (such as free-fall, orbital motion, and spacecraft trajectories), correspond to inertial motion within a curved geometry of spacetime in general relativity; there is no gravitational force deflecting objects from their natural, straight paths. Instead, gravity corresponds to changes in the properties of space and time, which in turn changes the straightest-possible paths that objects will naturally follow.^[34] The curvature is, in turn, caused by the energy–momentum of matter. Paraphrasing the relativist John Archibald Wheeler, spacetime tells matter how to move; matter tells spacetime how to curve.^[35]
While general relativity replaces the scalar gravitational potential of classical physics by a symmetric rank-two tensor, the latter reduces to the former in certain limiting cases. For weak gravitational fields and slow speed relative to the speed of light, the theory's predictions converge on those of Newton's law of universal gravitation.^[36]
As it is constructed using tensors, general relativity exhibits general covariance: its laws—and further laws formulated within the general relativistic framework—take on the same form in all coordinate systems.^[37] Furthermore, the theory does not contain any invariant geometric background structures, i.e. it is background independent. It thus satisfies a more stringent general principle of relativity, namely that the laws of physics are the same for all observers.^[38] Locally, as expressed in the equivalence principle, spacetime is Minkowskian, and the laws of physics exhibit local Lorentz invariance.^[39]

Model-building[edit]

The core concept of general-relativistic model-building is that of a solution of Einstein's equations. Given both Einstein's equations and suitable equations for the properties of matter, such a solution consists of a specific semi-Riemannian manifold (usually defined by giving the metric in specific coordinates), and specific matter fields defined on that manifold. Matter and geometry must satisfy Einstein's equations, so in particular, the matter's energy–momentum tensor must be divergence-free. The matter must, of course, also satisfy whatever additional equations were imposed on its properties. In short, such a solution is a model universe that satisfies the laws of general relativity, and possibly additional laws governing whatever matter might be present.^[40]
Einstein's equations are nonlinear partial differential equations and, as such, difficult to solve exactly.^[41] Nevertheless, a number of exact solutions are known, although only a few have direct physical applications.^[42] The best-known exact solutions, and also those most interesting from a physics point of view, are the Schwarzschild solution, the Reissner–Nordström solution and the Kerr metric, each corresponding to a certain type of black hole in an otherwise empty universe,^[43] and the Friedmann–Lemaître–Robertson–Walker and de Sitter universes, each describing an expanding cosmos.^[44] Exact solutions of great theoretical interest include the Gödel universe (which opens up the intriguing possibility of time travel in curved spacetimes), the Taub-NUT solution (a model universe that is homogeneous, but anisotropic), and anti-de Sitter space (which has recently come to prominence in the context of what is called the Maldacena conjecture).^[45]
Given the difficulty of finding exact solutions, Einstein's field equations are also solved frequently by numerical integration on a computer, or by considering small perturbations of exact solutions. In the field of numerical relativity, powerful computers are employed to simulate the geometry of spacetime and to solve Einstein's equations for interesting situations such as two colliding black holes.^[46] In principle, such methods may be applied to any system, given sufficient computer resources, and may address fundamental questions such as naked singularities. Approximate solutions may also be found by perturbation theories such as linearized gravity^[47] and its generalization, the post-Newtonian expansion, both of which were developed by Einstein. The latter provides a systematic approach to solving for the geometry of a spacetime that contains a distribution of matter that moves slowly compared with the speed of light. The expansion involves a series of terms; the first terms represent Newtonian gravity, whereas the later terms represent ever smaller corrections to Newton's theory due to general relativity.^[48] An extension of this expansion is the parametrized post-Newtonian (PPN) formalism, which allows quantitative comparisons between the predictions of general relativity and alternative theories.^[49]

Consequences of Einstein's theory[edit]

General relativity has a number of physical consequences. Some follow directly from the theory's axioms, whereas others have become clear only in the course of the ninety years of research that followed Einstein's initial publication.

Gravitational time dilation and frequency shift[edit]

Main article: Gravitational time dilation

Schematic representation of the gravitational redshift of a light wave escaping from the surface of a massive body

Assuming that the equivalence principle holds,^[50] gravity influences the passage of time. Light sent down into a gravity well is blueshifted, whereas light sent in the opposite direction (i.e., climbing out of the gravity well) is redshifted; collectively, these two effects are known as the gravitational frequency shift. More generally, processes close to a massive body run more slowly when compared with processes taking place farther away; this effect is known as gravitational time dilation.^[51]
Gravitational redshift has been measured in the laboratory^[52] and using astronomical observations.^[53] Gravitational time dilation in the Earth's gravitational field has been measured numerous times using atomic clocks,^[54] while ongoing validation is provided as a side effect of the operation of the Global Positioning System (GPS).^[55] Tests in stronger gravitational fields are provided by the observation of binary pulsars.^[56] All results are in agreement with general relativity.^[57] However, at the current level of accuracy, these observations cannot distinguish between general relativity and other theories in which the equivalence principle is valid.^[58]

Light deflection and gravitational time delay[edit]

Main articles: Kepler problem in general relativity, Gravitational lens and Shapiro delay

Deflection of light (sent out from the location shown in blue) near a compact body (shown in gray)

General relativity predicts that the path of light is bent in a gravitational field; light passing a massive body is deflected towards that body. This effect has been confirmed by observing the light of stars or distant quasars being deflected as it passes the Sun.^[59]
This and related predictions follow from the fact that light follows what is called a light-like or null geodesic—a generalization of the straight lines along which light travels in classical physics. Such geodesics are the generalization of the invariance of lightspeed in special relativity.^[60] As one examines suitable model spacetimes (either the exterior Schwarzschild solution or, for more than a single mass, the post-Newtonian expansion),^[61] several effects of gravity on light propagation emerge. Although the bending of light can also be derived by extending the universality of free fall to light,^[62] the angle of deflection resulting from such calculations is only half the value given by general relativity.^[63]
Closely related to light deflection is the gravitational time delay (or Shapiro delay), the phenomenon that light signals take longer to move through a gravitational field than they would in the absence of that field. There have been numerous successful tests of this prediction.^[64] In the parameterized post-Newtonian formalism (PPN), measurements of both the deflection of light and the gravitational time delay determine a parameter called γ, which encodes the influence of gravity on the geometry of space.^[65]

Gravitational waves[edit]

Main article: Gravitational wave

Ring of test particles influenced by gravitational wave

One of several analogies between weak-field gravity and electromagnetism is that, analogous to electromagnetic waves, there are gravitational waves: ripples in the metric of spacetime that propagate at the speed of light.^[66] The simplest type of such a wave can be visualized by its action on a ring of freely floating particles. A sine wave propagating through such a ring towards the reader distorts the ring in a characteristic, rhythmic fashion (animated image to the right).^[67] Since Einstein's equations are non-linear, arbitrarily strong gravitational waves do not obey linear superposition, making their description difficult. However, for weak fields, a linear approximation can be made. Such linearized gravitational waves are sufficiently accurate to describe the exceedingly weak waves that are expected to arrive here on Earth from far-off cosmic events, which typically result in relative distances increasing and decreasing by

10^{-21}

or less. Data analysis methods routinely make use of the fact that these linearized waves can be Fourier decomposed.^[68]
Some exact solutions describe gravitational waves without any approximation, e.g., a wave train traveling through empty space^[69] or so-called Gowdy universes, varieties of an expanding cosmos filled with gravitational waves.^[70] But for gravitational waves produced in astrophysically relevant situations, such as the merger of two black holes, numerical methods are presently the only way to construct appropriate models.^[71]

Orbital effects and the relativity of direction[edit]

Main article: Kepler problem in general relativity

General relativity differs from classical mechanics in a number of predictions concerning orbiting bodies. It predicts an overall rotation (precession) of planetary orbits, as well as orbital decay caused by the emission of gravitational waves and effects related to the relativity of direction.

Precession of apsides[edit]

Newtonian (red) vs. Einsteinian orbit (blue) of a lone planet orbiting a star

In general relativity, the apsides of any orbit (the point of the orbiting body's closest approach to the system's center of mass) will precess—the orbit is not an ellipse, but akin to an ellipse that rotates on its focus, resulting in a rose curve-like shape (see image). Einstein first derived this result by using an approximate metric representing the Newtonian limit and treating the orbiting body as a test particle. For him, the fact that his theory gave a straightforward explanation of the anomalous perihelion shift of the planet Mercury, discovered earlier by Urbain Le Verrier in 1859, was important evidence that he had at last identified the correct form of the gravitational field equations.^[72]
The effect can also be derived by using either the exact Schwarzschild metric (describing spacetime around a spherical mass)^[73] or the much more general post-Newtonian formalism.^[74] It is due to the influence of gravity on the geometry of space and to the contribution of self-energy to a body's gravity (encoded in the nonlinearity of Einstein's equations).^[75] Relativistic precession has been observed for all planets that allow for accurate precession measurements (Mercury, Venus, and Earth),^[76] as well as in binary pulsar systems, where it is larger by five orders of magnitude.^[77]

Orbital decay[edit]

Orbital decay for PSR1913+16: time shift in seconds, tracked over three decades.^[78]

According to general relativity, a binary system will emit gravitational waves, thereby losing energy. Due to this loss, the distance between the two orbiting bodies decreases, and so does their orbital period. Within the Solar System or for ordinary double stars, the effect is too small to be observable. This is not the case for a close binary pulsar, a system of two orbiting neutron stars, one of which is a pulsar: from the pulsar, observers on Earth receive a regular series of radio pulses that can serve as a highly accurate clock, which allows precise measurements of the orbital period. Because neutron stars are very compact, significant amounts of energy are emitted in the form of gravitational radiation.^[79]
The first observation of a decrease in orbital period due to the emission of gravitational waves was made by Hulse and Taylor, using the binary pulsar PSR1913+16 they had discovered in 1974. This was the first detection of gravitational waves, albeit indirect, for which they were awarded the 1993 Nobel Prize in physics.^[80] Since then, several other binary pulsars have been found, in particular the double pulsar PSR J0737-3039, in which both stars are pulsars.^[81]

Geodetic precession and frame-dragging[edit]

Main articles: Geodetic precession and Frame dragging

Several relativistic effects are directly related to the relativity of direction.^[82] One is geodetic precession: the axis direction of a gyroscope in free fall in curved spacetime will change when compared, for instance, with the direction of light received from distant stars—even though such a gyroscope represents the way of keeping a direction as stable as possible ("parallel transport").^[83] For the Moon–Earth system, this effect has been measured with the help of lunar laser ranging.^[84] More recently, it has been measured for test masses aboard the satellite Gravity Probe B to a precision of better than 0.3%.^[85]^[86]
Near a rotating mass, there are so-called gravitomagnetic or frame-dragging effects. A distant observer will determine that objects close to the mass get "dragged around". This is most extreme for rotating black holes where, for any object entering a zone known as the ergosphere, rotation is inevitable.^[87] Such effects can again be tested through their influence on the orientation of gyroscopes in free fall.^[88] Somewhat controversial tests have been performed using the LAGEOS satellites, confirming the relativistic prediction.^[89] Also the Mars Global Surveyor probe around Mars has been used.^[90]^[91]

Astrophysical applications[edit]

Gravitational lensing[edit]

Main article: Gravitational lensing

Einstein cross: four images of the same astronomical object, produced by a gravitational lens

The deflection of light by gravity is responsible for a new class of astronomical phenomena. If a massive object is situated between the astronomer and a distant target object with appropriate mass and relative distances, the astronomer will see multiple distorted images of the target. Such effects are known as gravitational lensing.^[92] Depending on the configuration, scale, and mass distribution, there can be two or more images, a bright ring known as an Einstein ring, or partial rings called arcs.^[93] The earliest example was discovered in 1979;^[94] since then, more than a hundred gravitational lenses have been observed.^[95] Even if the multiple images are too close to each other to be resolved, the effect can still be measured, e.g., as an overall brightening of the target object; a number of such "microlensing events" have been observed.^[96]
Gravitational lensing has developed into a tool of observational astronomy. It is used to detect the presence and distribution of dark matter, provide a "natural telescope" for observing distant galaxies, and to obtain an independent estimate of the Hubble constant. Statistical evaluations of lensing data provide valuable insight into the structural evolution of galaxies.^[97]

Gravitational wave astronomy[edit]

Main articles: Gravitational wave and Gravitational wave astronomy

Artist's impression of the space-borne gravitational wave detector LISA

Observations of binary pulsars provide strong indirect evidence for the existence of gravitational waves (see Orbital decay, above). However, gravitational waves reaching us from the depths of the cosmos have not been detected directly. Such detection is a major goal of current relativity-related research.^[98] Several land-based gravitational wave detectors are currently in operation, most notably the interferometric detectors GEO 600, LIGO (two detectors), TAMA 300 and VIRGO.^[99] Various pulsar timing arrays are using millisecond pulsars to detect gravitational waves in the 10⁻⁹ to 10⁻⁶ Hertz frequency range, which originate from binary supermassive blackholes.^[100] European space-based detector, eLISA / NGO, is currently under development,^[101] with a precursor mission (LISA Pathfinder) due for launch in 2015.^[102]
Observations of gravitational waves promise to complement observations in the electromagnetic spectrum.^[103] They are expected to yield information about black holes and other dense objects such as neutron stars and white dwarfs, about certain kinds of supernova implosions, and about processes in the very early universe, including the signature of certain types of hypothetical cosmic string.^[104]

Black holes and other compact objects[edit]

Main article: Black hole

Whenever the ratio of an object's mass to its radius becomes sufficiently large, general relativity predicts the formation of a black hole, a region of space from which nothing, not even light, can escape. In the currently accepted models of stellar evolution, neutron stars of around 1.4 solar masses, and stellar black holes with a few to a few dozen solar masses, are thought to be the final state for the evolution of massive stars.^[105] Usually a galaxy has one supermassive black hole with a few million to a few billion solar masses in its center,^[106] and its presence is thought to have played an important role in the formation of the galaxy and larger cosmic structures.^[107]

Simulation based on the equations of general relativity: a star collapsing to form a black hole while emitting gravitational waves

Astronomically, the most important property of compact objects is that they provide a supremely efficient mechanism for converting gravitational energy into electromagnetic radiation.^[108] Accretion, the falling of dust or gaseous matter onto stellar or supermassive black holes, is thought to be responsible for some spectacularly luminous astronomical objects, notably diverse kinds of active galactic nuclei on galactic scales and stellar-size objects such as microquasars.^[109] In particular, accretion can lead to relativistic jets, focused beams of highly energetic particles that are being flung into space at almost light speed.^[110] General relativity plays a central role in modelling all these phenomena,^[111] and observations provide strong evidence for the existence of black holes with the properties predicted by the theory.^[112]
Black holes are also sought-after targets in the search for gravitational waves (cf. Gravitational waves, above). Merging black hole binaries should lead to some of the strongest gravitational wave signals reaching detectors here on Earth, and the phase directly before the merger ("chirp") could be used as a "standard candle" to deduce the distance to the merger events–and hence serve as a probe of cosmic expansion at large distances.^[113] The gravitational waves produced as a stellar black hole plunges into a supermassive one should provide direct information about the supermassive black hole's geometry.^[114]

Cosmology[edit]

This blue horseshoe is a distant galaxy that has been magnified and warped into a nearly complete ring by the strong gravitational pull of the massive foreground luminous red galaxy.

Main article: Physical cosmology

The current models of cosmology are based on Einstein's field equations, which include the cosmological constant Λ since it has important influence on the large-scale dynamics of the cosmos,

R_{\mu\nu} - {\textstyle 1 \over 2}R\,g_{\mu\nu} + \Lambda\ g_{\mu\nu} = \frac{8\pi G}{c^{4}}\, T_{\mu\nu}

where $g_{\mu\nu}$ is the spacetime metric.^[115] Isotropic and homogeneous solutions of these enhanced equations, the Friedmann–Lemaître–Robertson–Walker solutions,^[116] allow physicists to model a universe that has evolved over the past 14 billion years from a hot, early Big Bang phase.^[117] Once a small number of parameters (for example the universe's mean matter density) have been fixed by astronomical observation,^[118] further observational data can be used to put the models to the test.^[119] Predictions, all successful, include the initial abundance of chemical elements formed in a period of primordial nucleosynthesis,^[120] the large-scale structure of the universe,^[121] and the existence and properties of a "thermal echo" from the early cosmos, the cosmic background radiation.^[122]
Astronomical observations of the cosmological expansion rate allow the total amount of matter in the universe to be estimated, although the nature of that matter remains mysterious in part. About 90% of all matter appears to be so-called dark matter, which has mass (or, equivalently, gravitational influence), but does not interact electromagnetically and, hence, cannot be observed directly.^[123] There is no generally accepted description of this new kind of matter, within the framework of known particle physics^[124] or otherwise.^[125] Observational evidence from redshift surveys of distant supernovae and measurements of the cosmic background radiation also show that the evolution of our universe is significantly influenced by a cosmological constant resulting in an acceleration of cosmic expansion or, equivalently, by a form of energy with an unusual equation of state, known as dark energy, the nature of which remains unclear.^[126]
A so-called inflationary phase,^[127] an additional phase of strongly accelerated expansion at cosmic times of around

10^{-33}

seconds, was hypothesized in 1980 to account for several puzzling observations that were unexplained by classical cosmological models, such as the nearly perfect homogeneity of the cosmic background radiation.^[128] Recent measurements of the cosmic background radiation have resulted in the first evidence for this scenario.^[129] However, there is a bewildering variety of possible inflationary scenarios, which cannot be restricted by current observations.^[130] An even larger question is the physics of the earliest universe, prior to the inflationary phase and close to where the classical models predict the big bang singularity. An authoritative answer would require a complete theory of quantum gravity, which has not yet been developed^[131] (cf. the section on quantum gravity, below).

Time travel[edit]

Kurt Gödel showed that closed timelike curve solutions to Einstein's equations exist which allow for loops in time. The solutions require extreme physical conditions unlikely ever to occur in practice, and it remains an open question whether further laws of physics will eliminate them completely. Since then other—similarly impractical—GR solutions containing CTCs have been found, such as the Tipler cylinder and traversable wormholes.

Advanced concepts[edit]

Causal structure and global geometry[edit]

Main article: Causal structure

Penrose–Carter diagram of an infinite Minkowski universe

In general relativity, no material body can catch up with or overtake a light pulse. No influence from an event A can reach any other location X before light sent out at A to X. In consequence, an exploration of all light worldlines (null geodesics) yields key information about the spacetime's causal structure. This structure can be displayed using Penrose–Carter diagrams in which infinitely large regions of space and infinite time intervals are shrunk ("compactified") so as to fit onto a finite map, while light still travels along diagonals as in standard spacetime diagrams.^[132]
Aware of the importance of causal structure, Roger Penrose and others developed what is known as global geometry. In global geometry, the object of study is not one particular solution (or family of solutions) to Einstein's equations. Rather, relations that hold true for all geodesics, such as the Raychaudhuri equation, and additional non-specific assumptions about the nature of matter (usually in the form of so-called energy conditions) are used to derive general results.^[133]

Horizons[edit]

Main articles: Horizon (general relativity), No hair theorem and Black hole mechanics

Using global geometry, some spacetimes can be shown to contain boundaries called horizons, which demarcate one region from the rest of spacetime. The best-known examples are black holes: if mass is compressed into a sufficiently compact region of space (as specified in the hoop conjecture, the relevant length scale is the Schwarzschild radius^[134]), no light from inside can escape to the outside. Since no object can overtake a light pulse, all interior matter is imprisoned as well. Passage from the exterior to the interior is still possible, showing that the boundary, the black hole's horizon, is not a physical barrier.^[135]

The ergosphere of a rotating black hole, which plays a key role when it comes to extracting energy from such a black hole

Early studies of black holes relied on explicit solutions of Einstein's equations, notably the spherically symmetric Schwarzschild solution (used to describe a static black hole) and the axisymmetric Kerr solution (used to describe a rotating, stationary black hole, and introducing interesting features such as the ergosphere). Using global geometry, later studies have revealed more general properties of black holes. In the long run, they are rather simple objects characterized by eleven parameters specifying energy, linear momentum, angular momentum, location at a specified time and electric charge. This is stated by the black hole uniqueness theorems: "black holes have no hair", that is, no distinguishing marks like the hairstyles of humans. Irrespective of the complexity of a gravitating object collapsing to form a black hole, the object that results (having emitted gravitational waves) is very simple.^[136]
Even more remarkably, there is a general set of laws known as black hole mechanics, which is analogous to the laws of thermodynamics. For instance, by the second law of black hole mechanics, the area of the event horizon of a general black hole will never decrease with time, analogous to the entropy of a thermodynamic system. This limits the energy that can be extracted by classical means from a rotating black hole (e.g. by the Penrose process).^[137] There is strong evidence that the laws of black hole mechanics are, in fact, a subset of the laws of thermodynamics, and that the black hole area is proportional to its entropy.^[138] This leads to a modification of the original laws of black hole mechanics: for instance, as the second law of black hole mechanics becomes part of the second law of thermodynamics, it is possible for black hole area to decrease—as long as other processes ensure that, overall, entropy increases. As thermodynamical objects with non-zero temperature, black holes should emit thermal radiation. Semi-classical calculations indicate that indeed they do, with the surface gravity playing the role of temperature in Planck's law. This radiation is known as Hawking radiation (cf. the quantum theory section, below).^[139]
There are other types of horizons. In an expanding universe, an observer may find that some regions of the past cannot be observed ("particle horizon"), and some regions of the future cannot be influenced (event horizon).^[140] Even in flat Minkowski space, when described by an accelerated observer (Rindler space), there will be horizons associated with a semi-classical radiation known as Unruh radiation.^[141]

Singularities[edit]

Main article: Spacetime singularity

Another general feature of general relativity is the appearance of spacetime boundaries known as singularities. Spacetime can be explored by following up on timelike and lightlike geodesics—all possible ways that light and particles in free fall can travel. But some solutions of Einstein's equations have "ragged edges"—regions known as spacetime singularities, where the paths of light and falling particles come to an abrupt end, and geometry becomes ill-defined. In the more interesting cases, these are "curvature singularities", where geometrical quantities characterizing spacetime curvature, such as the Ricci scalar, take on infinite values.^[142] Well-known examples of spacetimes with future singularities—where worldlines end—are the Schwarzschild solution, which describes a singularity inside an eternal static black hole,^[143] or the Kerr solution with its ring-shaped singularity inside an eternal rotating black hole.^[144] The Friedmann–Lemaître–Robertson–Walker solutions and other spacetimes describing universes have past singularities on which worldlines begin, namely Big Bang singularities, and some have future singularities (Big Crunch) as well.^[145]
Given that these examples are all highly symmetric—and thus simplified—it is tempting to conclude that the occurrence of singularities is an artifact of idealization.^[146] The famous singularity theorems, proved using the methods of global geometry, say otherwise: singularities are a generic feature of general relativity, and unavoidable once the collapse of an object with realistic matter properties has proceeded beyond a certain stage^[147] and also at the beginning of a wide class of expanding universes.^[148] However, the theorems say little about the properties of singularities, and much of current research is devoted to characterizing these entities' generic structure (hypothesized e.g. by the so-called BKL conjecture).^[149] The cosmic censorship hypothesis states that all realistic future singularities (no perfect symmetries, matter with realistic properties) are safely hidden away behind a horizon, and thus invisible to all distant observers. While no formal proof yet exists, numerical simulations offer supporting evidence of its validity.^[150]

Evolution equations[edit]

Main article: Initial value formulation (general relativity)

Each solution of Einstein's equation encompasses the whole history of a universe — it is not just some snapshot of how things are, but a whole, possibly matter-filled, spacetime. It describes the state of matter and geometry everywhere and at every moment in that particular universe. Due to its general covariance, Einstein's theory is not sufficient by itself to determine the time evolution of the metric tensor. It must be combined with a coordinate condition, which is analogous to gauge fixing in other field theories.^[151]
To understand Einstein's equations as partial differential equations, it is helpful to formulate them in a way that describes the evolution of the universe over time. This is done in so-called "3+1" formulations, where spacetime is split into three space dimensions and one time dimension. The best-known example is the ADM formalism.^[152] These decompositions show that the spacetime evolution equations of general relativity are well-behaved: solutions always exist, and are uniquely defined, once suitable initial conditions have been specified.^[153] Such formulations of Einstein's field equations are the basis of numerical relativity.^[154]

Global and quasi-local quantities[edit]

Main article: Mass in general relativity

The notion of evolution equations is intimately tied in with another aspect of general relativistic physics. In Einstein's theory, it turns out to be impossible to find a general definition for a seemingly simple property such as a system's total mass (or energy). The main reason is that the gravitational field—like any physical field—must be ascribed a certain energy, but that it proves to be fundamentally impossible to localize that energy.^[155]
Nevertheless, there are possibilities to define a system's total mass, either using a hypothetical "infinitely distant observer" (ADM mass)^[156] or suitable symmetries (Komar mass).^[157] If one excludes from the system's total mass the energy being carried away to infinity by gravitational waves, the result is the so-called Bondi mass at null infinity.^[158] Just as in classical physics, it can be shown that these masses are positive.^[159] Corresponding global definitions exist for momentum and angular momentum.^[160] There have also been a number of attempts to define quasi-local quantities, such as the mass of an isolated system formulated using only quantities defined within a finite region of space containing that system. The hope is to obtain a quantity useful for general statements about isolated systems, such as a more precise formulation of the hoop conjecture.^[161]

Relationship with quantum theory[edit]

If general relativity is considered as one of the two pillars of modern physics, quantum theory, the basis of understanding matter from elementary particles to solid state physics, is the other.^[162] However, it is still an open question as to how the concepts of quantum theory can be reconciled with those of general relativity.

Quantum field theory in curved spacetime[edit]

Main article: Quantum field theory in curved spacetime

Ordinary quantum field theories, which form the basis of modern elementary particle physics, are defined in flat Minkowski space, which is an excellent approximation when it comes to describing the behavior of microscopic particles in weak gravitational fields like those found on Earth.^[163] In order to describe situations in which gravity is strong enough to influence (quantum) matter, yet not strong enough to require quantization itself, physicists have formulated quantum field theories in curved spacetime. These theories rely on general relativity to describe a curved background spacetime, and define a generalized quantum field theory to describe the behavior of quantum matter within that spacetime.^[164] Using this formalism, it can be shown that black holes emit a blackbody spectrum of particles known as Hawking radiation, leading to the possibility that they evaporate over time.^[165] As briefly mentioned above, this radiation plays an important role for the thermodynamics of black holes.^[166]

Quantum gravity[edit]

Main article: Quantum gravity

The demand for consistency between a quantum description of matter and a geometric description of spacetime,^[167] as well as the appearance of singularities (where curvature length scales become microscopic), indicate the need for a full theory of quantum gravity: for an adequate description of the interior of black holes, and of the very early universe, a theory is required in which gravity and the associated geometry of spacetime are described in the language of quantum physics.^[168] Despite major efforts, no complete and consistent theory of quantum gravity is currently known, even though a number of promising candidates exist.^[169]

Projection of a Calabi–Yau manifold, one of the ways of compactifying the extra dimensions posited by string theory

Attempts to generalize ordinary quantum field theories, used in elementary particle physics to describe fundamental interactions, so as to include gravity have led to serious problems. At low energies, this approach proves successful, in that it results in an acceptable effective (quantum) field theory of gravity.^[170] At very high energies, however, the result are models devoid of all predictive power ("non-renormalizability").^[171]

Simple spin network of the type used in loop quantum gravity

One attempt to overcome these limitations is string theory, a quantum theory not of point particles, but of minute one-dimensional extended objects.^[172] The theory promises to be a unified description of all particles and interactions, including gravity;^[173] the price to pay is unusual features such as six extra dimensions of space in addition to the usual three.^[174] In what is called the second superstring revolution, it was conjectured that both string theory and a unification of general relativity and supersymmetry known as supergravity^[175] form part of a hypothesized eleven-dimensional model known as M-theory, which would constitute a uniquely defined and consistent theory of quantum gravity.^[176]
Another approach starts with the canonical quantization procedures of quantum theory. Using the initial-value-formulation of general relativity (cf. evolution equations above), the result is the Wheeler–deWitt equation (an analogue of the Schrödinger equation) which, regrettably, turns out to be ill-defined.^[177] However, with the introduction of what are now known as Ashtekar variables,^[178] this leads to a promising model known as loop quantum gravity. Space is represented by a web-like structure called a spin network, evolving over time in discrete steps.^[179]
Depending on which features of general relativity and quantum theory are accepted unchanged, and on what level changes are introduced,^[180] there are numerous other attempts to arrive at a viable theory of quantum gravity, some examples being dynamical triangulations,^[181] causal sets,^[182] twistor models^[183] or the path-integral based models of quantum cosmology.^[184]
All candidate theories still have major formal and conceptual problems to overcome. They also face the common problem that, as yet, there is no way to put quantum gravity predictions to experimental tests (and thus to decide between the candidates where their predictions vary), although there is hope for this to change as future data from cosmological observations and particle physics experiments becomes available.^[185]

Current status[edit]

General relativity has emerged as a highly successful model of gravitation and cosmology, which has so far passed many unambiguous observational and experimental tests. However, there are strong indications the theory is incomplete.^[186] The problem of quantum gravity and the question of the reality of spacetime singularities remain open.^[187] Observational data that is taken as evidence for dark energy and dark matter could indicate the need for new physics.^[188] Even taken as is, general relativity is rich with possibilities for further exploration. Mathematical relativists seek to understand the nature of singularities and the fundamental properties of Einstein's equations,^[189] and increasingly powerful computer simulations (such as those describing merging black holes) are run.^[190] The race for the first direct detection of gravitational waves continues,^[191] in the hope of creating opportunities to test the theory's validity for much stronger gravitational fields than has been possible to date.^[192] Almost a hundred years after its publication, general relativity remains a highly active area of research.^[193

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Wikipedia

Monday, January 20, 2014

Interstellar travel

From Wikipedia, the free encyclopedia

Contents

Difficulties

Required energy

Interstellar medium

Travel time

Interstellar distances

Communications

Prime targets for interstellar travel

Manned missions

Time dilation

Constant acceleration

Proposed methods

Slow manned missions

Generation ships

Suspended animation

Extended human lifespan

Frozen embryos

Island hopping through interstellar space

Faster manned missions

Unmanned

Nanoprobes

Ships with an external energy source

Propulsion

Rocket concepts

Nuclear fission powered

Fission-electric

Fission-fragment

Nuclear pulse

Nuclear fusion rockets

Antimatter rockets

Non-rocket concepts

Interstellar ramjets

Beamed propulsion

Pre-accelerated fuel

Speculative methods

Hawking radiation rockets

Magnetic monopole rockets

By transmission

Faster-than-light travel

Designs and studies

Project Hyperion

Enzmann starship

NASA research

Hundred-Year Starship study

See also

General relativity

Contents

History[edit]

From classical mechanics to general relativity[edit]

Geometry of Newtonian gravity[edit]

Relativistic generalization[edit]

Einstein's equations[edit]

Definition and basic applications[edit]

Definition and basic properties[edit]

Model-building[edit]

Consequences of Einstein's theory[edit]

Gravitational time dilation and frequency shift[edit]

Light deflection and gravitational time delay[edit]

Gravitational waves[edit]

Orbital effects and the relativity of direction[edit]

Precession of apsides[edit]

Orbital decay[edit]

Geodetic precession and frame-dragging[edit]

Astrophysical applications[edit]

Gravitational lensing[edit]

Gravitational wave astronomy[edit]

Black holes and other compact objects[edit]

Cosmology[edit]

Time travel[edit]

Advanced concepts[edit]

Causal structure and global geometry[edit]

Horizons[edit]

Singularities[edit]

Evolution equations[edit]

Global and quasi-local quantities[edit]