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Although the ITU now requires proof a satellite can be moved out of its orbital slot at the end of its lifespan, studies suggest this is insufficient. Despite efforts to reduce risk, spacecraft collisions have occurred. The European Space Agency telecom satellite Olympus-1 was struck by a meteoroid on 11 August and eventually moved to a graveyard orbit. As of October [update]it, and the upper stage of its launch rocket, were the oldest surviving artificial space objects still in orbit.

The satellites' BES-5 nuclear reactors were cooled with a coolant loop of sodium-potassium alloycreating a potential problem when the satellite reached end of life. While many satellites were nominally boosted into medium-altitude graveyard orbitsnot all were. Even satellites that had been properly moved to a higher orbit had an eight-percent probability of puncture and coolant release over a year period. The coolant freezes into droplets of solid sodium-potassium alloy, [61] forming additional debris.

Orbiting satellites have been deliberately destroyed. Space debris includes a glove lost by astronaut Ed White on the first American space-walk EVAa camera lost by Michael Collins near Gemini 10a thermal blanket lost during STSgarbage bags jettisoned by Soviet cosmonauts during Mir 's year life, [58] a wrench, and a toothbrush. In characterizing the problem of space debris, it was learned that much debris was due to rocket upper stages e.

Lower stages, like the Space Shuttle's Deflection - Delta Funktionen - Electromagnetic Radiation Part II (File) rocket boosters or Apollo program 's Saturn IB launch vehiclesdo not reach orbit. Launched on 28 February carrying an Arabsat-4A communications satelliteit malfunctioned before it could use up its propellant. Although the explosion was captured on film by astronomers, due to the orbit path the debris cloud has been difficult to measure with radar.

By 21 Februaryover 1, fragments were identified. The amount and size of the debris was unknown. In Decemberscientists confirmed that a previously detected near-Earth object, SOwas rocket booster space junk launched in orbiting Earth and the Sun. Program was shut down in The U. A test destroyed a 1-tonne 2, lb satellite orbiting at km micreating thousands of debris larger than 1 cm 0.

Due to the altitude, atmospheric drag decayed the orbit of most debris within a decade. A de facto moratorium followed the test. China's government was condemned for the military implications and the amount of debris from the anti-satellite missile test[83] the largest single space debris incident in history creating over 2, pieces golf-ball size or larger, over 35, 1 cm 0.

The target satellite orbited between km mi and km mithe portion of near-Earth space most densely populated with satellites. Brian Weeden, U. Air Force officer and Secure World Foundation staff member, noted that the Chinese satellite explosion created an orbital debris of more than 3, separate objects that then required tracking. The event occurred at about km miand the resulting debris has a perigee of km mi or lower.

He stated that the operation, part of Mission Shaktiwould defend the country's interests in space. Afterwards, US Air Force Space Command announced they were tracking new pieces of debris but expected the number to grow as data collection continues. The vulnerability of satellites to debris and the possibility of attacking LEO satellites to create debris clouds has triggered speculation that it is possible for countries unable to make a precision attack. Space junk can be a hazard to active satellites and spacecraft.

It has been theorized that Earth orbit could even become impassable if the risk of collision grows too high. However, since the risk to spacecraft increases with the time of exposure to high debris densities, it is more accurate to say that LEO would be rendered unusable by orbiting craft. The threat to craft passing through LEO to reach higher orbit would be much lower owing to the very short time span of the crossing.

Although spacecraft are typically protected by Whipple shieldssolar panels, which are exposed to the Sun, wear from low-mass impacts. Even small impacts can produce a cloud of plasma which is an electrical risk to the panels. Satellites are believed to have been destroyed by micrometeorites and small orbital debris MMOD. The earliest suspected loss was of Kosmoswhich disappeared on 24 July a month after launch. Kosmos contained no volatile propellant, therefore, there appeared to be nothing internal to the satellite which could have caused the destructive explosion which took place.

However, the case has not been proven and another hypothesis forwarded is that the battery exploded. Tracking showed it broke up, into new objects. Many impacts have been confirmed since. For example, on 24 Julythe French microsatellite Cerise was hit by fragments of an Ariane-1 H upper-stage booster which exploded in November It took nearly a month for the spacecraft to return to operation.

The first major satellite collision occurred on 10 February The kg 2, lb derelict satellite Kosmos and the operational kg 1, lb Iridium 33 collided, mi km [96] over northern Siberia.

The relative speed of impact was about Satellites sometimes [ clarification needed ] perform Collision Avoidance Maneuvers and satellite operators may monitor space debris as part of maneuver planning. For example, in Januarythe European Space Agency made the decision to alter orbit of one of its three [] Swarm mission spacecraft, based on data from the US Joint Space Operations Centerto lower the risk of collision from Cosmos, a derelict Russian satellite.

Crewed flights are naturally particularly sensitive to the hazards that could be presented by space debris conjunctions in the orbital path of the spacecraft.

Examples of occasional avoidance maneuvers, or longer-term space debris wear, have occurred in Space Shuttle missions, the MIR space station, and the International Space Station. One of the earliest events to publicize the debris problem occurred on Space Shuttle Challenger 's second flight, STS A fleck of paint struck its front window, creating a pit over 1 mm 0. On STS inEndeavour 's front window was pitted about half its depth.

Minor debris impacts increased from Window chipping and minor damage to thermal protection system tiles TPS were already common by the s. The Shuttle was later flown tail-first to take a greater proportion of the debris load on the engines and rear cargo bay, which are not used in orbit or during descent, and thus are less critical for post-launch operation.

When flying attached to the ISSthe two connected spacecraft were flipped around so the better-armored station shielded the orbiter. A NASA study concluded that debris accounted for approximately half of the overall risk to the Shuttle.

On a normal low-orbit mission to the ISS the risk was approximately 1 inbut the Hubble telescope repair mission was flown at the higher orbital altitude of km mi where the risk was initially calculated at a 1-in due in part to the satellite collision.

A re-analysis with better debris numbers reduced the estimated risk to 1 inand the mission went ahead. Debris incidents continued on later Shuttle missions. During STS in a fragment of circuit board bored a small hole through the radiator panels in Atlantis ' s cargo bay. Impact wear was notable on Mirthe Soviet space station, since it remained in space for long periods with its original solar module panels. The ISS also uses Whipple shielding to protect its interior from minor debris.

Inthe ISS panels were predicted to degrade approximately 0. As another method to reduce the risk to humans on board, ISS operational management asked the crew to shelter in the Soyuz on three occasions due to late debris-proximity warnings. In addition to the sixteen thruster firings and three Soyuz-capsule shelter orders, one attempted maneuver was not completed due to not having the several days' warning necessary to upload the maneuver timeline to the station's computer.

Kessler inis a theoretical scenario in which the density of objects in low Earth orbit LEO is high enough that collisions between objects could cause a cascade effect where each collision generates space debris that increases the likelihood of further collisions.

The growth in the number of objects as a result of the lates studies sparked debate in the space community on the nature of the problem and the earlier dire warnings. According to Kessler's derivation and updates, [] the LEO environment in the 1, km mi altitude range should be cascading. However, only one major satellite collision incident has occurred: the satellite collision between Iridium 33 and Cosmos The lack of obvious short-term cascading has led to speculation that the original estimates overstated the problem.

Although most debris burns up in the atmosphere, larger debris objects can reach the ground intact. According to NASA, an average of one cataloged piece of debris has fallen back to Earth each day for the past 50 years. Despite their size, there has been no significant property damage from the debris. Radar and optical detectors such as lidar are the main tools for tracking space debris.

Although objects under 10 cm 4 in have reduced orbital stability, debris as small as 1 cm can be tracked, [] [] however determining orbits to allow re-acquisition is difficult.

Most debris remain unobserved. Strategic Command keeps a catalog of known orbital objects, using ground-based radar and telescopes, and a space-based telescope originally to distinguish from hostile missiles.

The edition listed about 19, objects. Returned space hardware is a valuable source of information on the directional distribution and composition of the sub-millimetre debris flux. A debris cloud resulting from a single event is studied with scatter plots known as Gabbard diagrams, where the perigee and apogee of fragments are plotted with respect to their orbital period.

Gabbard diagrams of the early debris cloud prior to the effects of perturbations, if the data were available, are reconstructed. They often include data on newly observed, as yet uncatalogued fragments. Gabbard diagrams can provide important insights into the features of the fragmentation, the direction and point of impact. An average of about one tracked object per day has been dropping out of orbit for the past 50 years, [] averaging almost three objects per day at solar maximum due to the heating and expansion of the Earth's atmospherebut one about every three days at solar minimumusually five and a half years later.

A number of scholars have also observed that institutional factors —political, legal, economic, and cultural "rules of the game"—are the greatest impediment to the cleanup of near-Earth space. There is no commercial incentive, since costs aren't assigned to pollutersbut a number of suggestions have been made. In the US, governmental bodies have been accused of backsliding on previous commitments to limit debris growth, "let alone tackling the more complex issues of removing orbital debris.

As of the s, several technical approaches to the mitigation of the growth of space debris are typically undertaken, yet no comprehensive legal regime or cost assignment structure is in place to reduce space debris in the way that terrestrial pollution has reduced since the midth century. To avoid excessive creation of artificial space debris, many—but not all—satellites launched to above-low-Earth-orbit are launched initially into elliptical orbits with perigees inside Earth's atmosphere so the orbit will quickly decay and the satellites then will destroy themselves upon reentry into the atmosphere.

Other methods are used for spacecraft in higher orbits. These include passivation of the spacecraft at the end of its useful life; as well as the use of upper stages that can reignite to decelerate the stage to intentionally deorbit it, often on the first or second orbit following payload release; satellites that can, if they remain healthy for years, deorbit themselves from the lower orbits around Earth.

Other satellites such as many CubeSats in low orbits below approximately km mi orbital altitude depend on the energy-absorbing effects of the upper atmosphere to reliably deorbit a spacecraft within weeks or months. Increasingly, spent upper stages in higher orbits—orbits for which low-delta-v deorbit is not possible, or not planned for—and architectures that support satellite passivation, at end of life are passivated at end of life.

This removes any internal energy contained in the vehicle at the end of its mission or useful life. While this does not remove the debris of the now derelict rocket stage or satellite itself, it does substantially reduce the likelihood of the spacecraft destructing and creating many smaller pieces of space debris, a phenomenon that was common in many of the early generations of US and Soviet [62] spacecraft.

Upper stage passivation e. With a "one-up, one-down" launch-license policy for Earth orbits, launchers would rendezvous with, capture and de-orbit a derelict satellite from approximately the same orbital plane. Experiments have been flown by NASA, [] and SpaceX is developing large-scale on-orbit propellant Deflection - Delta Funktionen - Electromagnetic Radiation Part II (File) technology.

Another approach to debris mitigation is to explicitly design the mission architecture to always leave the rocket second-stage in an elliptical geocentric orbit with a low- perigeethus ensuring rapid orbital decay and avoiding long-term orbital debris from spent rocket bodies.

Such missions will often complete the payload placement in a final orbit by the use of low-thrust electric propulsion or with the use of a small kick stage to circularize the orbit. The kick stage itself may be designed with the excess-propellant capability to be able to self-deorbit.

Although the ITU requires geostationary satellites to move to a graveyard orbit at the end of their lives, the selected orbital areas do not sufficiently protect GEO lanes from debris. This was done with the French Spot-1 satellitereducing its atmospheric re-entry time from a projected years to about 15 by lowering its altitude from km mi to about km mi.

The Iridium constellation —95 communication satellites launched during the five-year period between and —provides a set of data points on the limits of self-removal. The satellite operator— Iridium Communications —remained operational albeit with a company name change through a corporate bankruptcy during the period over the two-decade life of the satellites, and by Decemberhad "completed disposal of the last of its 65 working legacy satellites. Passive methods of increasing the orbital decay rate of spacecraft debris have been proposed.

Instead of rockets, an electrodynamic tether could be attached to a spacecraft at launch; at the end of its lifetime, the tether would be rolled out to slow the spacecraft. A variety of approaches have been proposed, studied, or had ground subsystems built to use other spacecraft to remove existing space debris.

To date inremoval costs and legal questions about ownership and the authority to remove defunct satellites have stymied national or international action.

Current space law retains ownership of all satellites with their original operators, even debris or spacecraft which are defunct or threaten active missions. Moreover, as of [update]the cost of any of the proposed approaches for external removal is about the same as launching a spacecraft [ failed verification ] and, according to NASA's Nicholas Johnson, [ when? This began to change in the late s, as some companies made plans to begin to do external removal on their satellites in mid-LEO orbits.

For example, OneWeb planned to utilize onboard self-removal as "plan A" for satellite deorbiting at the end of life, but if a satellite were unable to remove itself within one year of end of life, OneWeb would implement "plan B" and dispatch a reusable multi-transport mission space tug to attach to the satellite at an already built-in capture target via a grappling fixture, to be towed to a lower orbit and released for re-entry.

A well-studied solution uses a remotely controlled vehicle to rendezvous with, capture, and return debris to a central station. A variation of this approach is for the remotely controlled vehicle to rendezvous with debris, capture it temporarily to attach a smaller de-orbit satellite and drag the debris with a tether to the desired location.

The "mothership" would then tow the debris-smallsat combination for atmospheric entry or move it to a graveyard orbit. On 7 January Star, Inc. In Decemberthe European Space Agency awarded the first contract to clean up space debris.

A "chaser" will grab the junk with four robotic arms and drag it down to Earth's atmosphere where both will burn up. The laser broom uses a ground-based laser to ablate the front of the debris, producing a rocket-like thrust that slows the object. With continued application, the debris would fall enough to be influenced by atmospheric drag. Air Force's Project Orion was a laser-broom design.

There's a reason why it's been sitting on the shelf for more than a decade. The momentum of the laser-beam photons could directly impart a thrust on the debris sufficient to move small debris into new orbits out of the way of working satellites. NASA research in indicates that firing a laser beam at a piece of space junk could impart an impulse of 1 mm 0.

The launch was an operational test only. Sincethe European Space Agency has been working on the design of a mission to remove large space debris from orbit. The mission, e. Deorbitis scheduled for launch during with an objective to remove debris heavier than 4, kilograms 8, lb from LEO.

In order to complete its planned experiments the platform is equipped with a net, a harpoon, a laser ranging instrument, a dragsail, and two CubeSats miniature research satellites. There is no international treaty minimizing space debris. As ofthe committee was discussing international "rules of the road" to prevent collisions between satellites. Inthe European Space Agency ESA worked with an international group to promulgate a similar set of standards, also with a "year rule" applying to most Earth-orbit satellites and upper stages.

Germany and France have posted bonds to safeguard the property from debris damage. Bythe Indian Space Research Organization ISRO had developed a number of technical means of debris mitigation upper stage passivation, propellant reserves for movement to graveyard orbits, etc.

Inthe ISO began preparing an international standard for space-debris mitigation. However, these standards are not binding on any party by ISO or any international jurisdiction.

They are simply available for use in any of a variety of voluntary ways. They "can be adopted voluntarily by a spacecraft manufacturer or operator, or brought into effect through a commercial contract between a customer and supplier, or used as the basis for establishing a set of national regulations on space debris mitigation.

The voluntary ISO standard also adopted the "year rule" for the "LEO protected region" below 2, km 1, mi altitude that has been previously and still is, as of [update] used by the US, ESA, and UN mitigation standards, and identifies it as "an upper limit for the amount of time that a space system shall remain in orbit after its mission is completed.

Ideally, the time to deorbit should be as short as possible i. Holger Krag of the European Space Agency states that as of there is no binding international regulatory framework with no progress occurring at the respective UN body in Vienna. Until the End of the World is a French sci-fi drama set under the backdrop of an out-of-control Indian nuclear satellite, predicted to re-enter the atmosphere, threatening vast populated areas of the Earth.

In the Planetesa Japanese hard science fiction manga and animethe story revolves around the crew of a space debris collection craft in the year Gravitya survival film directed by Alfonso Cuaronis about a disaster on a space mission caused by Kessler syndrome. From Wikipedia, the free encyclopedia.

For other uses, see Space Junk disambiguation. Pollution around Earth by defunct artificial objects. Air pollution. In fact, despite newer technologies, the cathode ray tube, or CRTstill forms the backbone of the video display industry.

Invented by German scientist Karl Ferdinand Braun init has seen many advances since then. Essentially the device consists of a glass vacuum tube in which an image is generated when a negatively charged plate called a cathode is heated so it emits electrons.

These electrons are focused and beamed onto a surface coated with phosphorwhich glows when hit by radiation. To get this glow and therefore the image to appear across an entire screen, the beam of electrons must be deflected to every possible spot across the screen.

Most smaller CRTs use electrostatic deflectionwhich occurs when the electron beam is deflected as it passes through charged metal plates; the direction of deflection depends on the amount of charge and polarity of the plates.

Below is illustrated electromagnetic deflectionmore common in TVs, computer screens and other larger CRTS, which uses magnets to move the electron beam. The tutorial, a simplified depiction of how a CRT works, can be set on automatic or adjusted manually by clicking the appropriate radio button. When the tutorial is in manual mode, the beam of electrons emitted by the cathode in the electron gun will hit the center of the screen until one of the two external magnets is moved.

Click and drag the magnets to move them closer to and farther away from the beam of electrons. Notice that moving one magnet vertically deflects the electrons horizontallyand vice versa. All tensors are written in abstract index notation. In general relativity, the world line of a particle free from all external, non-gravitational force is a particular type of geodesic in curved spacetime.

In other words, a freely moving or falling particle always moves along a geodesic. The geodesic equation is:. The quantity on the left-hand-side of this equation is the acceleration of a particle, and so this equation is analogous to Newton's laws of motion which likewise provide formulae for the acceleration of a particle. This equation of motion employs the Einstein notationmeaning that repeated indices are summed i. The Christoffel symbols are functions of the four spacetime coordinates, and so are independent of the velocity or acceleration or other characteristics of a test particle whose motion is described by the geodesic equation.

In general relativity, the effective gravitational potential energy of an object of mass m rotating around a massive central body M is given by [41] [42]. A conservative total force can then be obtained as [ citation needed ]. The first term represents the Newton's force of gravitywhich is described by the inverse-square law.

The second term represents the centrifugal force in the circular motion. The third term represents the relativistic effect.

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. General relativity is a metric theory of gravitation.

At its core are Einstein's equationswhich describe the relation between the geometry of a four-dimensional pseudo-Riemannian manifold representing spacetime, and the energy—momentum contained in that spacetime. 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.

Paraphrasing the relativist John Archibald Wheelerspacetime tells matter how to move; matter tells spacetime how to curve. While general relativity replaces the scalar gravitational potential of classical physics by a symmetric rank -two tensorthe 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. 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.

It thus satisfies a more stringent general principle of relativitynamely that the laws of physics are the same for all observers. 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 coordinatesand 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.

Einstein's equations are nonlinear partial differential equations and, as such, difficult to solve exactly. 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 relativitypowerful computers are employed to simulate the geometry of spacetime and to solve Einstein's equations for interesting situations such as two colliding black holes.

Approximate solutions may also be found by perturbation theories such as linearized gravity [58] and its generalization, the post-Newtonian expansionboth 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. 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 many years of research that followed Einstein's initial publication. Assuming that the equivalence principle holds, [61] gravity influences the passage of time. Light sent down into a gravity well is blueshiftedwhereas light sent in the opposite direction i. 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.

Gravitational redshift has been measured in the laboratory [63] and using astronomical observations. General relativity predicts that the path of light will follow the curvature of spacetime as it passes near a star.

This effect was initially confirmed by observing the light of stars or distant quasars being deflected as it passes the Sun. 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. Although the bending of light can also be derived by extending the universality of free fall to light, [73] the angle of deflection resulting from such calculations is only half the value given by general relativity.

Closely related to light deflection is the gravitational time delay or Shapiro delaythe 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. Predicted in [77] [78] by Albert Einstein, there are gravitational waves: ripples in the metric of spacetime that propagate at the speed of light. These are one of several analogies between weak-field gravity and electromagnetism in that, they are analogous to electromagnetic waves.

On February 11,the Advanced LIGO team announced that they had directly detected gravitational waves from a pair of black holes merging. 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.

Data analysis methods routinely make use of the fact that these linearized waves can be Fourier decomposed.

Some exact solutions describe gravitational waves without any approximation, e. 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.

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 ellipsebut 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 Mercury's anomalous perihelion shift, discovered earlier by Urbain Le Verrier inwas important evidence that he had at last identified the correct form of the gravitational field equations.

The effect can also be derived by using either the exact Schwarzschild metric describing spacetime around a spherical mass [88] or the much more general post-Newtonian formalism. According to general relativity, a binary system will emit gravitational waves, thereby losing energy. Due to this Deflection - Delta Funktionen - Electromagnetic Radiation Part II (File), the distance between the two orbiting bodies decreases, and so does their orbital period. Within the Solar System or for ordinary double starsthe effect is too small to be observable.

This is not the case for a close binary pulsar, a system of two orbiting neutron starsone 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 immensely compact, significant amounts of energy are emitted in the form of gravitational radiation.

This was the first detection of gravitational waves, albeit indirect, for which they were awarded the Nobel Prize in physics. Several relativistic effects are directly related to the relativity of direction. Near a rotating mass, there are 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 ergosphererotation is inevitable. Examples of prominent physicists who support neo-Lorentzian explanations of general relativity are Franco Selleri and Antony Valentini. 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. Gravitational lensing has developed into a tool of observational astronomy. It is used to detect the presence and distribution of dark matterprovide 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. Observations of binary pulsars provide strong indirect evidence for the existence of gravitational waves see Orbital decayabove. Detection of these waves is a major goal of current relativity-related research. Observations of gravitational waves promise to complement observations in the electromagnetic spectrum. 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 evolutionneutron stars of around 1. Astronomically, the most important property of compact objects is that they provide a supremely efficient mechanism for converting gravitational energy into electromagnetic radiation. Black holes are also sought-after targets in the search for gravitational waves cf. Gravitational wavesabove. 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.

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.

An authoritative answer would require a complete theory of quantum gravity, which has not yet been developed [] cf.

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. It is logical to ask what symmetries if any might apply in General Relativity. A tractable case might be to consider the symmetries of spacetime as seen by observers located far away from all sources of the gravitational field.

The naive expectation for asymptotically flat spacetime symmetries might be simply to extend and reproduce the symmetries of flat spacetime of special relativity, viz. In Hermann Deflection - Delta Funktionen - Electromagnetic Radiation Part II (File)M. Metzner [] and Rainer K. Sachs [] addressed this asymptotic symmetry problem in order to investigate the flow of energy at infinity due to propagating gravitational waves. Their first step was to decide on some physically sensible boundary conditions to place on the gravitational field at light-like infinity to characterize what it means to say a metric is asymptotically flat, making no a priori assumptions about the nature of the asymptotic symmetry group — not even the assumption that such a group exists.

Then after designing what they considered to be the most sensible boundary conditions, they investigated the nature of the resulting asymptotic symmetry transformations that leave invariant the form of the boundary conditions appropriate for asymptotically flat gravitational fields.

What they found was that the asymptotic symmetry transformations actually do form a group and the structure of this group does not depend on the particular gravitational field that happens to be present.

This means that, as expected, one can separate the kinematics of spacetime from the dynamics of the gravitational field at least at spatial infinity.

Not only are the Lorentz transformations asymptotic symmetry transformations, there are also additional transformations that are not Lorentz transformations but are asymptotic symmetry transformations. In fact, they found an additional infinity of transformation generators known as supertranslations.

This implies the conclusion that General Relativity GR does not reduce to special relativity in the case of weak fields at long distances. It turns out that the BMS symmetry, suitably modified, could be seen as a restatement of the universal soft graviton theorem in quantum field theory QFTwhich relates universal infrared soft QFT with GR asymptotic spacetime symmetries.

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.

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 equationand additional non-specific assumptions about the nature of matter usually in the form of energy conditions are used to derive general results.

Using global geometry, some spacetimes can be shown to contain boundaries called horizonswhich 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 conjecturethe relevant length scale is the Schwarzschild radius []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 horizonis not a physical barrier.

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. With time they become rather simple objects characterized by eleven parameters specifying: electric charge, mass-energy, linear momentumangular momentumand location at a specified time.

This is stated by the black hole uniqueness theorem : "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.

Even more remarkably, there is a general set of laws known as black hole mechanicswhich 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. 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. There are other types of horizons.

In an expanding universe, an observer may find that some regions of the past cannot be observed " Deflection - Delta Funktionen - Electromagnetic Radiation Part II (File) horizon "and some regions of the future cannot be influenced event horizon. 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 singularitieswhere 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 scalartake on infinite values.

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. While no formal proof yet exists, numerical simulations offer supporting evidence of its validity.

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 conditionwhich is analogous to gauge fixing in other field theories.

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. The best-known example is the ADM formalism.

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.


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