General relativity
${\displaystyle G_{\mu \nu }+\mathrm{\Lambda }{g}_{\mu \nu }=\kappa T_{\mu \nu }}$
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Tests of general relativity serve to establish observational evidence for thetheory of general relativity. The first three tests, proposed byAlbert Einstein in 1915, concerned the "anomalous"precession of theperihelion ofMercury, the bending of light ingravitational fields, and thegravitational redshift. The precession of Mercury was already known; experiments showing light bending in accordance with the predictions ofgeneral relativity were performed in 1919, with increasingly precise measurements made in subsequent tests; and scientists claimed to have measured the gravitational redshift in 1925, although measurements sensitive enough to actually confirm the theory were not made until 1954. A more accurate program starting in 1959 tested general relativity in the weak gravitational field limit, severely limiting possible deviations from the theory.

In the 1970s, scientists began to make additional tests, starting withIrwin Shapiro's measurement of the relativistic time delay in radar signal travel time near the Sun. Beginning in 1974,Hulse,Taylor and others studied the behaviour ofbinary pulsars experiencing much stronger gravitational fields than those found in the Solar System. Both in the weak field limit (as in the Solar System) and with the stronger fields present in systems of binary pulsars the predictions of general relativity have been extremely well tested.

In February 2016, theAdvanced LIGO team announced that they haddirectly detected gravitational waves from a black hole merger.^[1] This discovery, along with additional detections announced in June 2016 and June 2017,^[2] tested general relativity in the very strong field limit, observing to date no deviations from theory.

Albert Einstein proposed^[3][4] three tests of general relativity, subsequently called the "classical tests" of general relativity, in 1916:

1. the perihelion precession ofMercury's orbit
2. thedeflection of light by theSun
3. thegravitational redshift of light

In the letter toThe Times (of London) on November 28, 1919, he described the theory of relativity and thanked his English colleagues for their understanding and testing of his work. He also mentioned three classical tests with comments:^[5]

"The chief attraction of the theory lies in its logical completeness. If a single one of the conclusions drawn from it proves wrong, it must be given up; to modify it without destroying the whole structure seems to be impossible."

UnderNewtonian physics, an object in an (isolated) two-body system, consisting of the object orbiting a spherical mass, would trace out anellipse with the center of mass of the system at afocus of the ellipse. The point of closest approach, called theperiapsis (or when the central body is the Sun,perihelion), is fixed. Hence the major axis of the ellipse remains fixed in space. Both objects orbit around the center of mass of this system, so they each have their own ellipse. However, a number of effects in the Solar System cause the perihelia of planets to precess (rotate) around the Sun in the plane of their orbits, or equivalently, cause the major axis to rotate about the center of mass, hence changing its orientation in space.^[6] The principal cause is the presence of other planets whichperturb one another's orbit. Another (much less significant) effect is solaroblateness.

Mercury deviates from the precession predicted from these Newtonian effects. This anomalous rate of precession of the perihelion of Mercury's orbit was first recognized in 1859 as a problem incelestial mechanics, byUrbain Le Verrier. His re-analysis of available timed observations of transits of Mercury over the Sun's disk from 1697 to 1848 showed that the actual rate of the precession disagreed from that predicted from Newton's theory by 38″ (arcseconds) pertropical century (later re-estimated at 43″ bySimon Newcomb in 1882).^[7] A number ofad hoc and ultimately unsuccessful solutions were proposed, but they tended to introduce more problems. Le Verrier suggested that another hypothetical planet might exist to account for Mercury's behavior.^[7] The previously successful search for Neptune based on its perturbations of the orbit of Uranus led astronomers to place some faith in this possible explanation, and the hypothetical planet was even namedVulcan. Finally, in 1908,W. W. Campbell, Director of the Lick Observatory, after the comprehensive photographic observations by Lick astronomer,Charles D. Perrine, at three solar eclipse expeditions, stated, "In my opinion, Dr. Perrine's work at the three eclipses of 1901, 1905, and 1908 brings the observational side of the famous intramercurial-planet problem definitely to a close."^[8][9] Subsequently, no evidence of Vulcan was found and Einstein's 1915 general theory accounted for Mercury's anomalous precession. Einstein wrote toMichele Besso, "Perihelion motions explained quantitatively ... you will be astonished".^[10]

In general relativity, this remainingprecession, or change of orientation of the orbital ellipse within its orbital plane, is explained by gravitation being mediated by the curvature of spacetime. Einstein showed that general relativity^[3] agrees closely with the observed amount of perihelion shift. This was a powerful factor motivating the adoption of general relativity.

Although earlier measurements of planetary orbits were made using conventional telescopes, more accurate measurements are now made withradar. The total observed precession of Mercury is (574.10 ± 0.65)″ per century^[11] relative to the inertialICRF. This precession can be attributed to the following causes:

The correction by (42.980±0.001)″/cy is the prediction ofpost-Newtonian theory withparameters${\displaystyle \gamma =\beta =1}$.^[13] Thus the effect can be fully explained by general relativity. More recent calculations based on more precise measurements have not materially changed the situation.

In general relativity the perihelion shiftσ, expressed in radians per revolution, is approximately given by:^[14]

${\displaystyle \sigma =\frac{24{\pi }^3{L}^2}{T^2{c}^2\left(1-e^2\right)},}$

whereL is thesemi-major axis,T is theorbital period,c is the speed of light, ande is theorbital eccentricity (see:Two-body problem in general relativity).

The other planets experience perihelion shifts as well, but, since they are farther from the Sun and have longer periods, their shifts are lower, and could not be observed accurately until long after Mercury's. For example, the perihelion shift of Earth's orbit due to general relativity is theoretically 3.83868″ per century and experimentally (3.8387±0.0004)″/cy, Venus's is 8.62473″/cy and (8.6247 ± 0.0005)″/cy and Mars' is (1.351±0.001)″/cy. Both values have now been measured, with results in good agreement with theory.^[15] Theperiapsis shift has also now been measured for binary pulsar systems, withPSR 1913+16 amounting to 4.2° per year.^[16] These observations are consistent with general relativity.^[17] It is also possible to measure periapsis shift in binary star systems which do not contain ultra-dense stars, but it is more difficult to model the classical effects precisely – for example, the alignment of the stars' spin to their orbital plane needs to be known and is hard to measure directly. A few systems, such asDI Herculis,^[18] have been measured as test cases for general relativity.

Henry Cavendish in 1784 (in an unpublished manuscript) andJohann Georg von Soldner in 1801 (published in 1804) had pointed out that Newtonian gravity predicts that starlight will bend around a massive object.^[19][20] The same value as Soldner's was calculated by Einstein in 1911 based on the equivalence principle alone. However, Einstein noted in 1915 in the process of completing general relativity, that his 1911 result (and thus Soldner's 1801 result) is only half of the correct value. Einstein became the first to calculate the correct value for light bending: 1.75arcseconds for light that grazes the Sun.^[21][22]

The first observation of light deflection was performed by noting the change in position ofstars as they passed near the Sun on thecelestial sphere. The observations were performed byArthur Eddington and his collaborators (seeEddington experiment) during the totalsolar eclipse of May 29, 1919,^[23] when the stars near the Sun (at that time in the constellationTaurus) could be observed.^[23] Observations were made simultaneously in the cities ofSobral, Ceará, Brazil and inSão Tomé and Príncipe on the west coast of Africa.^[24] The result was considered spectacular news and made the front page of most major newspapers. It made Einstein and his theory of general relativity world-famous. When asked by his assistant what his reaction would have been if general relativity had not been confirmed by Eddington and Dyson in 1919, Einstein famously made the quip: "Then I would feel sorry for the dear Lord. The theory is correct anyway."^[25]

The early accuracy, however, was poor and there was doubt that the small number of measured star locations and instrument questions could produce a reliable result. The results were argued by some^[26] to have been plagued bysystematic error and possiblyconfirmation bias, although modern reanalysis of the dataset^[27] suggests that Eddington's analysis was accurate.^[28][29] The measurement was repeated by a team from theLick Observatory led by the DirectorW. W. Campbell in the1922 eclipse as observed in remote Australian station ofWallal,^[30] with results based on hundreds of star positions that agreed with the 1919 results^[29] and has been repeated several times since, most notably in 1953 byYerkes Observatory astronomers^[31] and in 1973 by a team from theUniversity of Texas.^[32] Considerable uncertainty remained in these measurements for almost fifty years, until observations started being made atradio frequencies.^[33][34] The deflection of starlight by the nearbywhite dwarf starStein 2051 B has also been measured.^[35]

Einstein predicted thegravitational redshift of light from theequivalence principle in 1907, and it was predicted that this effect might be measured in the spectral lines of awhite dwarf star, which has a very high gravitational field. Initial attempts to measure the gravitational redshift of the spectrum ofSirius-B were done byWalter Sydney Adams in 1925, but the result was criticized as being unusable due to the contamination from light from the (much brighter) primary star,Sirius.^[36][37] The first accurate measurement of the gravitational redshift of a white dwarf was done by Popper in 1954, measuring a 21 km/s gravitational redshift of40 Eridani B.^[37]

The redshift of Sirius B was finally measured by Greensteinet al. in 1971, obtaining the value for the gravitational redshift of89±16 km/s, with more accurate measurements by the Hubble Space Telescope showing80.4±4.8 km/s.^[38]

The general theory of relativity incorporates Einstein'sspecial theory of relativity, and hence tests of special relativity are also testing aspects of general relativity. As a consequence of theequivalence principle,Lorentz invariance holds locally in non-rotating, freely falling reference frames. Experiments related to Lorentz invariance special relativity (that is, when gravitational effects can be neglected) are described intests of special relativity.

The modern era of testing general relativity was ushered in largely at the impetus ofDicke andSchiff who laid out a framework for testing general relativity.^[39][40][41] They emphasized the importance not only of the classical tests, but of null experiments, testing for effects which in principle could occur in a theory of gravitation, but do not occur in general relativity. Other important theoretical developments included the inception ofalternative theories to general relativity, in particular,scalar–tensor theories such as theBrans–Dicke theory;^[42] theparameterized post-Newtonian formalism in which deviations from general relativity can be quantified; and the framework of theequivalence principle.

Experimentally, new developments inspace exploration,electronics andcondensed matter physics have made additional precise experiments possible, such as the Pound–Rebka experiment, laser interferometry andlunar rangefinding.

Early tests of general relativity were hampered by the lack of viable competitors to the theory: it was not clear what sorts of tests would distinguish it from its competitors. General relativity was the only known relativistic theory of gravity compatible with special relativity and observations. This changed in 1960 with the introduction ofBrans–Dicke theory which provided an alternative theory also in agreement with experimental observations.^[43]: 3 Ultimately, this led to the development of theparametrized post-Newtonian formalism byNordtvedt andWill, which parametrizes, in terms of ten adjustable parameters, all the possible departures from Newton's law of universal gravitation to first order in the velocity of moving objects (i.e. to first order in${\displaystyle v/c}$, wherev is the velocity of an object andc is the speed of light). This approximation allows the possible deviations from general relativity, for slowly moving objects in weak gravitational fields, to be systematically analyzed. Much effort has been put into constraining the post-Newtonian parameters, and deviations from general relativity are at present severely limited.

The experiments testing gravitational lensing and light time delay limits the same post-Newtonian parameter, the so-called Eddington parameter γ, which is a straightforward parametrization of the amount of deflection of light by a gravitational source. It is equal to one for general relativity, and takes different values in other theories (such as Brans–Dicke theory). It is the best constrained of the ten post-Newtonian parameters, but there are other experiments designed to constrain the others. Precise observations of the perihelion shift of Mercury constrain other parameters, as do tests of the strong equivalence principle.

One of the goals of theBepiColombo mission to Mercury, is to test the general relativity theory by measuring the parameters gamma and beta of the parametrized post-Newtonian formalism with high accuracy.^[44][45] The experiment is part of the Mercury Orbiter Radio science Experiment (MORE).^[46][47] The spacecraft was launched in October 2018 and is expected to enter orbit around Mercury in December 2025.

One of the most important tests isgravitational lensing. It has been observed in distant astrophysical sources, but these are poorly controlled and it is uncertain how they constrain general relativity. The most precise tests are analogous to Eddington's 1919 experiment: they measure the deflection of radiation from a distant source by the Sun. The sources that can be most precisely analyzed are distantradio sources. In particular, somequasars are very strong radio sources. The directional resolution of any telescope is in principle limited by diffraction; for radio telescopes this is also the practical limit. An important improvement in obtaining positional high accuracies (from milli-arcsecond to micro-arcsecond) was obtained by combining radio telescopes across Earth. The technique is calledvery long baseline interferometry (VLBI). With this technique radio observations couple the phase information of the radio signal observed in telescopes separated over large distances. Recently, these telescopes have measured the deflection of radio waves by the Sun to extremely high precision, confirming the amount of deflection predicted by general relativity aspect to the 0.03% level.^[48] At this level of precision systematic effects have to be carefully taken into account to determine the precise location of the telescopes on Earth. Some important effects are Earth'snutation, rotation, atmospheric refraction, tectonic displacement and tidal waves. Another important effect is refraction of the radio waves by thesolar corona. Fortunately, this effect has a characteristicspectrum, whereas gravitational distortion is independent of wavelength. Thus, careful analysis, using measurements at several frequencies, can subtract this source of error.

The entire sky is slightly distorted due to the gravitational deflection of light caused by the Sun (the anti-Sun direction excepted). This effect has been observed by theEuropean Space Agency astrometric satelliteHipparcos. It measured the positions of about 10⁵ stars. During the full mission about3.5×10⁶ relative positions have been determined, each to an accuracy of typically 3 milliarcseconds (the accuracy for an 8–9 magnitude star). Since the gravitation deflection perpendicular to the Earth–Sun direction is already 4.07 milliarcseconds, corrections are needed for practically all stars. Without systematic effects, the error in an individual observation of 3 milliarcseconds, could be reduced by the square root of the number of positions, leading to a precision of 0.0016 milliarcseconds. Systematic effects, however, limit the accuracy of the determination to 0.3% (Froeschlé, 1997).

Launched in 2013, theGaia spacecraft will conduct a census of one billionstars in theMilky Way and measure their positions to an accuracy of 24 microarcseconds. Thus it will also provide stringent new tests of gravitational deflection of light caused by theSun which was predicted by General relativity.^[49]

Irwin I. Shapiro proposed another test, beyond the classical tests, which could be performed within the Solar System. It is sometimes called the fourth "classical" test ofgeneral relativity. He predicted a relativistic time delay (Shapiro delay) in the round-trip travel time for radar signals reflecting off other planets.^[50] The mere curvature of the path of aphoton passing near the Sun is too small to have an observable delaying effect (when the round-trip time is compared to the time taken if the photon had followed a straight path), but general relativity predicts a time delay that becomes progressively larger when the photon passes nearer to the Sun due to thetime dilation in thegravitational potential of the Sun. Observing radar reflections from Mercury and Venus just before and after they are eclipsed by the Sun agrees with general relativity theory at the 5% level.^[51]

More recently, theCassini probe has undertaken a similar experiment which gave agreement with general relativity at the 0.002% level.^[52] However, the following detailed studies^[53][54] revealed that the measured value of the PPN parameter gamma is affected by agravitomagnetic effect caused by the orbital motion of Sun around thebarycenter of the solar system. The gravitomagnetic effect in theCassini radioscience experiment was implicitly postulated by B. Bertotti as having a pure general relativistic origin but its theoretical value has never been tested in the experiment which effectively makes the experimental uncertainty in the measured value of gamma actually larger (by a factor of 10) than 0.002% claimed by B. Bertotti and co-authors in Nature.

Very Long Baseline Interferometry has measured velocity-dependent (gravitomagnetic) corrections to the Shapiro time delay in the field of moving Jupiter^[55][56] and Saturn.^[57]

The equivalence principle, in its simplest form, asserts that the trajectories of falling bodies in a gravitational field should be independent of their mass and internal structure, provided they are small enough not to disturb the environment or be affected bytidal forces. This idea has been tested to extremely high precision byEötvös torsion balance experiments, which look for a differential acceleration between two test masses. Constraints on this, and on the existence of a composition-dependent fifth force or gravitationalYukawa interaction are very strong, and are discussed underfifth force andweak equivalence principle.

A version of the equivalence principle, called thestrong equivalence principle, asserts that self-gravitation falling bodies, such as stars, planets or black holes (which are all held together by their gravitational attraction) should follow the same trajectories in a gravitational field, provided the same conditions are satisfied. This is called theNordtvedt effect and is most precisely tested by theLunar Laser Ranging Experiment.^[58][59] Since 1969, it has continuously measured the distance from several rangefinding stations on Earth to reflectors on the Moon to approximately centimeter accuracy.^[60] These have provided a strong constraint on several of the other post-Newtonian parameters.

Another part of the strong equivalence principle is the requirement that Newton's gravitational constant be constant in time, and have the same value everywhere in the universe. There are many independent observations limiting the possible variation of Newton'sgravitational constant,^[61] but one of the best comes from lunar rangefinding which suggests that the gravitational constant does not change by more than one part in 10¹¹ per year. The constancy of the other constants is discussed in theEinstein equivalence principle section of the equivalence principle article.

The first of the classical tests discussed above, thegravitational redshift, is a simple consequence of theEinstein equivalence principle and was predicted by Einstein in 1907. As such, it is not a test of general relativity in the same way as the post-Newtonian tests, because any theory of gravity obeying the equivalence principle should also incorporate the gravitational redshift. Nonetheless, confirming the existence of the effect was an important substantiation of relativistic gravity, since the absence of gravitational redshift would have strongly contradicted relativity. The first observation of the gravitational redshift was the measurement of the shift in the spectral lines from thewhite dwarf starSirius B by Adams in 1925, discussed above, and follow-on measurements of other white dwarfs. Because of the difficulty of the astrophysical measurement, however, experimental verification using a known terrestrial source was preferable.

Experimental verification of gravitational redshift using terrestrial sources took several decades, because it is difficult to find clocks (to measuretime dilation) or sources of electromagnetic radiation (to measure redshift) with a frequency that is known well enough that the effect can be accurately measured. It was confirmed experimentally for the first time in 1959 using measurements of the change in wavelength of gamma-ray photons generated with theMössbauer effect, which generates radiation with a very narrow line width. ThePound–Rebka experiment measured the relative redshift of two sources situated at the top and bottom of Harvard University's Jefferson tower.^[62][63] The result was in excellent agreement with general relativity. This was one of the first precision experiments testing general relativity. The experiment was later improved to better than the 1% level by Pound and Snider.^[64]

The blueshift of a falling photon can be found by assuming it has an equivalent mass based on its frequencyE =hf (whereh is thePlanck constant) along withE =mc², a result of special relativity. Such simple derivations ignore the fact that in general relativity the experiment compares clock rates, rather than energies. In other words, the "higher energy" of the photon after it falls can be equivalently ascribed to the slower running of clocks deeper in the gravitational potential well. To fully validate general relativity, it is important to also show that the rate of arrival of the photons is greater than the rate at which they are emitted. A very accurate gravitational redshift experiment, which deals with this issue, was performed in 1976,^[65] where ahydrogenmaser clock on a rocket was launched to a height of 10,000 km, and its rate compared with an identical clock on the ground. It tested the gravitational redshift to 0.007%.

Although theGlobal Positioning System (GPS) is not designed as a test of fundamental physics, it must account for the gravitational redshift in its timing system, and physicists have analyzed timing data from the GPS to confirm other tests. When the first satellite was launched, some engineers resisted the prediction that a noticeable gravitational time dilation would occur, so the first satellite was launched without the clock adjustment that was later built into subsequent satellites. It showed the predicted shift of 38 microseconds per day. This rate of discrepancy is sufficient to substantially impair function of GPS within hours if not accounted for. An excellent account of the role played by general relativity in the design of GPS can be found in Ashby 2003.^[66]

Other precision tests of general relativity,^[67] not discussed here, are theGravity Probe A satellite, launched in 1976, which showed gravity and velocity affect the ability to synchronize the rates of clocks orbiting a central mass and theHafele–Keating experiment, which used atomic clocks in circumnavigating aircraft to test general relativity and special relativity together.^[68][69]

Tests of theLense–Thirring precession, consisting of small secularprecessions of the orbit of a test particle in motion around a central rotating mass, for example, a planet or a star, have been performed with theLAGEOS satellites,^[70] but many aspects of them remain controversial. The same effect may have been detected in the data of theMars Global Surveyor (MGS) spacecraft, a former probe in orbit aroundMars; also such a test raised a debate.^[71] First attempts to detect theSun's Lense–Thirring effect on theperihelia of the innerplanets have been recently reported as well. Frame dragging would cause the orbital plane of stars orbiting near asupermassive black hole to precess about the black hole spin axis. This effect should be detectable within the next few years viaastrometric monitoring of stars at the center of theMilky Way galaxy.^[72] By comparing the rate of orbital precession of two stars on different orbits, it is possible in principle to test theno-hair theorems of general relativity.^[73]

TheGravity Probe B satellite, launched in 2004 and operated until 2005, detected frame-dragging and thegeodetic effect. The experiment used four quartz spheres the size of ping pong balls coated with a superconductor. Data analysis continued through 2011 due to high noise levels and difficulties in modelling the noise accurately so that a useful signal could be found. Principal investigators atStanford University reported on May 4, 2011, that they had accurately measured the frame dragging effect relative to the distant starIM Pegasi, and the calculations proved to be in line with the prediction of Einstein's theory. The results, published inPhysical Review Letters measured thegeodetic effect with an error of about 0.2 percent. The results reported the frame dragging effect (caused by Earth's rotation) added up to 37 milliarcseconds with an error of about 19 percent.^[74] Investigator Francis Everitt explained that a milliarcsecond "is the width of a human hair seen at the distance of 10 miles".^[75]

In January 2012,LARES satellite was launched on aVega rocket^[76] to measureLense–Thirring effect with an accuracy of about 1%, according to its proponents.^[77] This evaluation of the actual accuracy obtainable is a subject of debate.^[78][79][80]

It is possible to test whether the gravitational potential continues with the inverse square law at very small distances. Tests so far have focused on a divergence from GR in the form of aYukawa potential$V(r)=V_0\left(1+\alpha e^{-r/\lambda }\right)$, but no evidence for a potential of this kind has been found. The Yukawa potential with${\displaystyle \alpha =1}$ has been ruled out down toλ =5.6×10⁻⁵ m.^[81]

It was conceived as a means to measure thetime dilation effect on Earth after being motivated by Einstein'sequivalence principle that implies a rotating observer will be subject to the same transformations as an observer in a gravitational field.^[82] Mössbauer rotor experiments hence permit a precise terrestrial test of therelativistic Doppler effect. From a radioactive source fixed at the center of a spinning disc or rod,gamma rays travel to an absorber at the rim (in some variations of the experiment this scheme was reversed) and an unabsorbed number of them pass through depending on the rotational speed to arrive at a stationary counter (i.e., detector of gamma quanta resting in the lab frame). In lieu with theClock hypothesis, Einstein'sgeneral relativity predicts that the moving absorber's clock at the rim should retard by a specific amount due to time dilation on account of centrifugal binding alone compared to a rest frame absorber. So the transmission of gamma photons through the absorber should increase during rotation, which can be subsequently measured by the stationary counter beyond the absorber. This prediction was actually observed using theMössbauer effect, since the equivalence principle, as originally suggested by Einstein, implicitly allows the association of the time dilation due to rotation (calculated as a result of the change in the detector's count rate) with gravitational time dilation. Such experiments were pioneered by Hayet al. (1960),^[83] Champeneyet al. (1965),^[84] and Kündig (1963),^[85] and all of them had declared confirmation of the prediction of Einstein's theory of relativity.

Be that as it may, an early 21st Century re-examination of these endeavors called into question the validity of the past obtained results claiming to have verified time dilation as predicted by Einstein's relativity theory,^[86][87] whereby novel experimentations were carried out that uncovered anextra energy shift between emitted and absorbed radiation next to the classical relativistic dilation of time.^[88][89] This discovery was first explained as discreditinggeneral relativity and successfully confirming at the laboratory scale the predictions of an alternative theory of gravity developed by T. Yarman and his colleagues.^[90] Against this development, a contentious attempt was made to explain the disclosed extra energy shift as arising from a so-far unknown and allegedly missedclock synchronization effect,^[91][92] which was unusually awarded a prize in 2018 by theGravity Research Foundation for having secureda new proof of general relativity.^[93] However, at the same time period, it was revealed that said author committed several mathematical errors in his calculations,^[94] and the supposed contribution of the so-called clock synchronization to the measured time dilation is in fact practically null.^{[95][96][97][98][99][100]} As a consequence, a general relativistic explanation for the outcomes of Mössbauer rotor experiments remains open.

The very strong gravitational fields that are present close toblack holes, especially thosesupermassive black holes which are thought to poweractive galactic nuclei and the more activequasars, belong to a field of intense active research. Observations of these quasars and active galactic nuclei are difficult, and interpretation of the observations is heavily dependent upon astrophysical models other than general relativity or competing fundamentaltheories of gravitation, but they are qualitatively consistent with the black hole concept as modeled in general relativity.

Pulsars are rapidly rotatingneutron stars which emit regular radio pulses as they rotate. As such they act as clocks which allow very precise monitoring of their orbital motions. Observations of pulsars in orbit around other stars have all demonstrated substantialperiapsis precessions that cannot be accounted for classically but can be accounted for by using general relativity. For example, the Hulse–Taylorbinary pulsarPSR B1913+16 (a pair of neutron stars in which one is detected as a pulsar) has an observed precession of over 4° of arc per year (periastron shift per orbit only about 10⁻⁶). This precession has been used to compute the masses of the components.

Similarly to the way in which atoms and molecules emit electromagnetic radiation, a gravitating mass that is inquadrupole type or higher order vibration, or is asymmetric and in rotation, can emit gravitational waves.^[101] Thesegravitational waves are predicted to travel at thespeed of light. For example, planets orbiting the Sun constantly lose energy via gravitational radiation, but this effect is so small that it is unlikely it will be observed in the near future (Earth radiates about 200 watts ofgravitational radiation).

The radiation of gravitational waves has been inferred from theHulse–Taylor binary (and other binary pulsars).^[102] Precise timing of the pulses shows that the stars orbit only approximately according toKepler's Laws: over time they gradually spiral towards each other, demonstrating anenergy loss in close agreement with the predicted energy radiated by gravitational waves.^[103][104] For their discovery of the first binary pulsar and measuring its orbital decay due to gravitational-wave emission,Hulse andTaylor won the 1993Nobel Prize in Physics.^[105]

A "double pulsar" discovered in 2003,PSR J0737-3039, has a periastron precession of 16.90° per year; unlike the Hulse–Taylor binary, bothneutron stars are detected as pulsars, allowing precision timing of both members of the system. Due to this, the tight orbit, the fact that the system is almost edge-on, and the very low transverse velocity of the system as seen from Earth, J0737−3039 provides by far the best system for strong-field tests of general relativity known so far. Several distinct relativistic effects are observed, including orbital decay as in the Hulse–Taylor system. After observing the system for two and a half years, four independent tests of general relativity were possible, the most precise (the Shapiro delay) confirming the general relativity prediction within 0.05%^[106] (nevertheless the periastron shift per orbit is only about 0.0013% of a circle and thus it is not a higher-order relativity test).

In 2013, an international team of astronomers reported new data from observing a pulsar-white dwarf systemPSR J0348+0432, in which they have been able to measure a change in the orbital period of 8 millionths of a second per year, and confirmed GR predictions in a regime of extreme gravitational fields never probed before;^[107] but there are still some competing theories that would agree with these data.^[108]

A number ofgravitational-wave detectors have been built with the intent of directly detecting the gravitational waves emanating from such astronomical events as the merger of twoneutron stars orblack holes. In February 2016, theAdvanced LIGO team announced that they haddirectly detected gravitational waves from a stellarbinary black hole merger,^{[1][109][110]} with additional detections announced in June 2016, June 2017, and August 2017.^[2][111]

General relativity predicts gravitational waves, as does any theory of gravitation in which changes in the gravitational field propagate at a finite speed.^[112] Then, the LIGO response function could discriminate among the various theories.^[113][114] Since gravitational waves can be directly detected,^[1][110] it is possible to use them to learn about the Universe. This isgravitational-wave astronomy. Gravitational-wave astronomy can test general relativity by verifying that the observed waves are of the form predicted (for example, that they only have two transverse polarizations), and by checking thatblack holes are the objects described by solutions of theEinstein field equations.^{[115][116][117]}

Gravitational-wave astronomy can also test Maxwell-Einstein field equations. This version of the field equations predicts that spinning magnetars (i.e., neutron stars with extremely strong magnetic dipole field) should emit gravitational waves.^[118]

"These amazing observations are the confirmation of a lot of theoretical work, including Einstein's general theory of relativity, which predicts gravitational waves", said Stephen Hawking.^[1]

The galaxy M87 was the subject of observation by theEvent Horizon Telescope (EHT) in 2017; the 10 April 2019 issue ofAstrophysical Journal Letters (vol. 875, No. 1) was dedicated to the EHT results, publishing sixopen-access papers. Theevent horizon of the black hole at the center of M87 was directly imaged at the wavelength of radio waves by the EHT; the image was revealed in a press conference on 10 April 2019, the first image of a black hole's event horizon.^[120][119]In May 2022, the EHT provided the first image of the super massive black hole Sagittarius A* in the center of our own Milky Way galaxy.

Gravitational redshift in light from theS2 star orbiting the supermassive black holeSagittarius A* in the center of the Milky Way has been measured with theVery Large Telescope using GRAVITY, NACO and SIFONI instruments.^[121][122] Additionally, there has now been detection of the Schwarzschild precession in the orbit of the star S2 near the Galactic centre massive black hole.^[123]

The strong equivalence principle of general relativity requires universality of free fall to apply even to bodies with strong self-gravity. Direct tests of this principle using Solar System bodies are limited by the weak self-gravity of the bodies, and tests using pulsar–white-dwarf binaries have been limited by the weak gravitational pull of the Milky Way. With the discovery of a triple star system calledPSR J0337+1715, located about 4,200 light-years from Earth, the strong equivalence principle can be tested with a high accuracy. This system contains aneutron star in a 1.6-day orbit with awhite dwarf star, and the pair in a 327-day orbit with another white dwarf further away. This system permits a test that compares how the gravitational pull of the outer white dwarf affects the pulsar, which has strong self-gravity, and the inner white dwarf. The result shows that the accelerations of the pulsar and its nearby white-dwarf companion differ fractionally by no more than 2.6×10⁻⁶ (95%confidence level).^{[124][125][126]}

This technique is based on the idea thatphoton trajectories are modified in the presence of a gravitational body. A very common astrophysical system in the universe is ablack hole surrounded by anaccretion disk. The radiation from the general neighborhood, including the accretion disk, is affected by the nature of the central black hole. Assuming Einstein's theory is correct, astrophysical black holes are described by the Kerr metric. (A consequence of theno-hair theorems.) Thus, by analyzing the radiation from such systems, it is possible to test Einstein's theory.

Most of the radiation from these black hole – accretion disk systems (e.g.,black hole binaries andactive galactic nuclei) arrives in the form of X-rays. When modeled, the radiation is decomposed into several components. Tests of Einstein's theory are possible with the thermal spectrum (only for black hole binaries) and the reflection spectrum (for both black hole binaries and active galactic nuclei). The former is not expected to provide strong constraints,^[127] while the latter is much more promising.^[128] In both cases, systematic uncertainties might make such tests more challenging.^[129]

Tests of general relativity on the largest scales are not nearly so stringent as Solar System tests.^[130] The earliest such test was the prediction and discovery of theexpansion of the universe.^[131] In 1922,Alexander Friedmann found that the Einstein equations have non-stationary solutions (even in the presence of thecosmological constant).^[132][133] In 1927,Georges Lemaître showed that static solutions of the Einstein equations, which are possible in the presence of the cosmological constant, are unstable, and therefore the static universe envisioned by Einstein could not exist (it must either expand or contract).^[132] Lemaître made an explicit prediction that the universe should expand.^[134] He also derived a redshift-distance relationship, which is now known as theHubble Law.^[134] Later, in 1931, Einstein himself agreed with the results of Friedmann and Lemaître.^[132] The expansion of the universe discovered byEdwin Hubble in 1929^[132] was then considered by many (and continues to be considered by some now) as a direct confirmation of general relativity.^[135] In the 1930s, largely due to the work ofE. A. Milne, it was realised that the linear relationship between redshift and distance derives from the general assumption of uniformity and isotropy rather than specifically from general relativity.^[131] However the prediction of a non-static universe was non-trivial, indeed dramatic, and primarily motivated by general relativity.^[136]

Some other cosmological tests include searches for primordial gravitational waves generated duringcosmic inflation, which may be detected in thecosmic microwave backgroundpolarization^[137] or by a proposed space-basedgravitational-wave interferometer called theBig Bang Observer. Other tests at high redshift are constraints on other theories of gravity,^[138][139] and the variation of the gravitational constant sinceBig Bang nucleosynthesis (it varied by no more than 40% since then).^{[citation needed]}

In August 2017, the findings of tests conducted by astronomers using theEuropean Southern Observatory'sVery Large Telescope (VLT), among other instruments, were released, and positively demonstrated gravitational effects predicted by Albert Einstein. One of these tests observed the orbit of the stars circling aroundSagittarius A*, a black hole about 4 million times as massive as the sun. Einstein's theory suggested that large objects bend the space around them, causing other objects to diverge from the straight lines they would otherwise follow. Although previous studies have validated Einstein's theory, this was the first time his theory had been tested on such a gigantic object. The findings were published inThe Astrophysical Journal.^[140][141]

Astronomers using the Hubble Space Telescope and the Very Large Telescope have made precise tests of general relativity on galactic scales. The nearby galaxyESO 325-G004 acts as a strong gravitational lens, distorting light from a distant galaxy behind it to create anEinstein ring around its centre. By comparing the mass of ESO 325-G004 (from measurements of the motions of stars inside this galaxy) with the curvature of space around it, astronomers found that gravity behaves as predicted by general relativity on these astronomical length-scales.^[142][143]

• General relativity
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• the USENET Relativity FAQ experiments page
• Mathpages article on Mercury's perihelion shift (for amount of observed and GR shifts).

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