Tests of general relativity

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Tests of general relativity serve to establish observational evidence for the

perihelion of Mercury, the bending of light in gravitational fields, and the gravitational redshift. The precession of Mercury was already known; experiments showing light bending in accordance with the predictions of general 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 with

Taylor and others studied the behaviour of binary 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, the

directly 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.

Classical tests

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

  1. the perihelion precession of Mercury's orbit
  2. the deflection of light by the Sun
  3. the gravitational redshift of light

In the letter to The 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."

Perihelion precession of Mercury

Further information: Two-body problem in general relativity
Transit of Mercury on November 8, 2006 with sunspots #921, 922, and 923
The perihelion precession of Mercury

Under

oblateness
.

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 to Michael Besso, "Perihelion motions explained quantitatively ... you will be astonished".[10]

In general relativity, this remaining

precession, 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 with

ICRF
. This precession can be attributed to the following causes:

Sources of the precession of perihelion for Mercury
Amount (arcsec/Julian century)[12] Cause
532.3035 gravitational tugs of other solar bodies
0.0286 oblateness of the Sun (quadrupole moment)
42.9799 gravitoelectric effects (Schwarzschild-like), a general relativity effect
−0.0020 Lense–Thirring precession
575.31[12] total predicted
574.10 ± 0.65[11] observed

The correction by (42.980 ± 0.001)″/cy is the prediction of post-Newtonian theory with parameters .[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 shift σ, expressed in radians per revolution, is approximately given by:[14]

where L is the

semi-major axis, T is the orbital period, c is the speed of light, and e is the orbital 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.

PSR 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 as DI Herculis,[18]
have been measured as test cases for general relativity.

Deflection of light by the Sun

Eddington's photographs of the 1919 solar eclipse experiment
, presented in his 1920 paper announcing its success

arcseconds for light that grazes the Sun.[21][22]

The first observation of light deflection was performed by noting the change in position of

Arthur Eddington and his collaborators (see Eddington experiment) during the total solar eclipse of May 29, 1919,[23] when the stars near the Sun (at that time in the constellation Taurus) could be observed.[23] Observations were made simultaneously in the cities of Sobral, Ceará, Brazil and in São 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

University of Texas.[32] Considerable uncertainty remained in these measurements for almost fifty years, until observations started being made at radio frequencies.[33][34]
The deflection of starlight by the nearby
Stein 2051 B has also been measured.[35]

Gravitational redshift of light

Main article: Gravitational redshift § Experimental verification
The gravitational redshift of a light wave as it moves upwards against a gravitational field (caused by the yellow star below).

Einstein predicted the

Sirius-B, were done by Walter 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 of 40 Eridani B.[37]

The redshift of Sirius B was finally measured by Greenstein et al. in 1971, obtaining the value for the gravitational redshift of 89±16 km/s, with more accurate measurements by the Hubble Space Telescope showing 80.4±4.8 km/s.[38]

Tests of special relativity

See also: Tests of special relativity

The general theory of relativity incorporates Einstein's

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 in tests of special relativity
.

Modern tests

The modern era of testing general relativity was ushered in largely at the impetus of

Schiff 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 of alternative theories to general relativity, in particular, scalar–tensor theories such as the Brans–Dicke theory;[42] the parameterized post-Newtonian formalism in which deviations from general relativity can be quantified; and the framework of the equivalence principle
.

Experimentally, new developments in

lunar rangefinding
.

Post-Newtonian tests of gravity

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. Moreover, it is an extremely simple and elegant theory.[

parametrized post-Newtonian formalism by Nordtvedt and Will
, 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 , where v is the velocity of an object and c 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 the BepiColombo 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.[43][44] The experiment is part of the Mercury Orbiter Radio science Experiment (MORE).[45][46] The spacecraft was launched in October 2018 and is expected to enter orbit around Mercury in December 2025.

Gravitational lensing

One of the most important tests is

solar corona. Fortunately, this effect has a characteristic spectrum
, 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 the European Space Agency astrometric satellite Hipparcos. It measured the positions of about 105 stars. During the full mission about 3.5×106 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, the Gaia spacecraft will conduct a census of one billion stars in the Milky 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 the Sun which was predicted by General relativity.[48]

Light travel time delay testing

Main article: Shapiro time delay

Shapiro delay) in the round-trip travel time for radar signals reflecting off other planets.[49] The mere curvature of the path of a photon 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 the time dilation in the gravitational 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.[50]

More recently, the

barycenter of the solar system. The gravitomagnetic effect in the Cassini
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[54][55] and Saturn.[56]

Equivalence principle

Main article: Equivalence principle

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 by

weak equivalence principle
.

A version of the equivalence principle, called the

Lunar Laser Ranging Experiment.[57][58] Since 1969, it has continuously measured the distance from several rangefinding stations on Earth to reflectors on the Moon to approximately centimeter accuracy.[59]
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's

Einstein equivalence principle
section of the equivalence principle article.

Gravitational redshift and time dilation

Main articles: Gravitational redshift and Gravitational time dilation
Further information: Clock drift § Relativity

The first of the classical tests discussed above, the

Einstein 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 the white dwarf star Sirius
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 measure time 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 the Mössbauer effect, which generates radiation with a very narrow line width. The Pound–Rebka experiment measured the relative redshift of two sources situated at the top and bottom of Harvard University's Jefferson tower.[61][62] 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.[63]

The blueshift of a falling photon can be found by assuming it has an equivalent mass based on its frequency E = hf (where h is the Planck constant) along with E = 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,[64] where a hydrogen maser 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 the Global 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.[65]

Other precision tests of general relativity,[66] not discussed here, are the Gravity 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 the Hafele–Keating experiment, which used atomic clocks in circumnavigating aircraft to test general relativity and special relativity together.[67][68]

Frame-dragging tests

The LAGEOS-1 satellite. (D=60 cm)
Main article: Frame-dragging

Tests of the

perihelia of the inner planets have been recently reported as well. Frame dragging would cause the orbital plane of stars orbiting near a supermassive black hole to precess about the black hole spin axis. This effect should be detectable within the next few years via astrometric monitoring of stars at the center of the Milky Way galaxy.[71] By comparing the rate of orbital precession of two stars on different orbits, it is possible in principle to test the no-hair theorems of general relativity.[72]

The Gravity Probe B satellite, launched in 2004 and operated until 2005, detected frame-dragging and the geodetic 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 at Stanford University reported on May 4, 2011, that they had accurately measured the frame dragging effect relative to the distant star IM Pegasi, and the calculations proved to be in line with the prediction of Einstein's theory. The results, published in Physical Review Letters measured the geodetic 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.[73] Investigator Francis Everitt explained that a milliarcsecond "is the width of a human hair seen at the distance of 10 miles".[74]

In January 2012,

Lense–Thirring effect with an accuracy of about 1%, according to its proponents.[76] This evaluation of the actual accuracy obtainable is a subject of debate.[77][78][79]

Tests of the gravitational potential at small distances

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 a Yukawa potential , but no evidence for a potential of this kind has been found. The Yukawa potential with has been ruled out down to λ = 5.6×10−5 m.[80]

Mössbauer rotor experiment

It was conceived as a means to measure the

Clock hypothesis, Einstein's general 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 the Mössbauer 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 Hay et al. (1960),[82] Champeney et al. (1965),[83] and Kündig (1963),[84]
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,[85][86] whereby novel experimentations were carried out that uncovered an extra energy shift between emitted and absorbed radiation next to the classical relativistic dilation of time.[87][88] This discovery was first explained as discrediting general relativity and successfully confirming at the laboratory scale the predictions of an alternative theory of gravity developed by T. Yarman and his colleagues.[89] Against this development, a contentious attempt was made to explain the disclosed extra energy shift as arising from a so-far unknown and allegedly missed clock synchronization effect,[90][91] which was unusually awarded a prize in 2018 by the Gravity Research Foundation for having secured a new proof of general relativity.[92] However, at the same time period, it was revealed that said author committed several mathematical errors in his calculations,[93] and the supposed contribution of the so-called clock synchronization to the measured time dilation is in fact practically null.[94][95][96][97][98][99] As a consequence, a general relativistic explanation for the outcomes of Mössbauer rotor experiments remains open.

Strong field tests

The very strong gravitational fields that are present close to

active galactic nuclei and the more active quasars, 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 fundamental theories of gravitation
, but they are qualitatively consistent with the black hole concept as modeled in general relativity.

Binary pulsars

Further information: Binary pulsar

PSR 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 in

gravitational waves are predicted to travel at the speed 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 of gravitational radiation
).

The radiation of gravitational waves has been inferred from the

Taylor won the 1993 Nobel Prize in Physics.[104]

A "double pulsar" discovered in 2003,

PSR J0737-3039, has a periastron precession of 16.90° per year; unlike the Hulse–Taylor binary, both neutron 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%[105]
(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 system PSR 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;[106] but there are still some competing theories that would agree with these data.[107]

Direct detection of gravitational waves

A number of

directly detected gravitational waves from a stellar binary black hole merger,[1][108][109] with additional detections announced in June 2016, June 2017, and August 2017.[2][110]

General relativity predicts gravitational waves, as does any theory of gravitation in which changes in the gravitational field propagate at a finite speed.[111] Then, the LIGO response function could discriminate among the various theories.[112][113] Since gravitational waves can be directly detected,[1][109] it is possible to use them to learn about the Universe. This is gravitational-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 that black holes are the objects described by solutions of the Einstein field equations.[114][115][116]

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.[117]

"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]

Direct observation of black holes

A bright ring of material surrounding a dark center that marks the shadow of the M87's supermassive black hole. The image also provided a key confirmation of General relativity.[118]

The galaxy M87 was the subject of observation by the

open-access papers. The event 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.[119][118]
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 and orbit precession of star in strong gravity field

Gravitational redshift in light from the S2 star orbiting the supermassive black hole Sagittarius A* in the center of the Milky Way has been measured with the Very Large Telescope using GRAVITY, NACO and SIFONI instruments.[120][121] Additionally, there has now been detection of the Schwarzschild precession in the orbit of the star S2 near the Galactic centre massive black hole.[122]

Strong equivalence principle

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 called PSR J0337+1715, located about 4,200 light-years from Earth, the strong equivalence principle can be tested with a high accuracy. This system contains a neutron star in a 1.6-day orbit with a white 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).[123][124][125]

X-ray spectroscopy

This technique is based on the idea that photon trajectories are modified in the presence of a gravitational body. A very common astrophysical system in the universe is a black hole surrounded by an accretion 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 the no-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 and active 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,[126] while the latter is much more promising.[127] In both cases, systematic uncertainties might make such tests more challenging.[128]

Cosmological tests

Tests of general relativity on the largest scales are not nearly so stringent as Solar System tests.

E. 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.[130] However the prediction of a non-static universe was non-trivial, indeed dramatic, and primarily motivated by general relativity.[135]

Some other cosmological tests include searches for primordial gravitational waves generated during

gravitational-wave interferometer called the Big Bang Observer. Other tests at high redshift are constraints on other theories of gravity,[137][138] and the variation of the gravitational constant since Big Bang nucleosynthesis (it varied by no more than 40% since then).[citation needed
]

In August 2017, the findings of tests conducted by astronomers using the European Southern Observatory's Very 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 around Sagittarius 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 in The Astrophysical Journal.[139][140]

Gravitational lensing

Astronomers using the Hubble Space Telescope and the Very Large Telescope have made precise tests of general relativity on galactic scales. The nearby galaxy ESO 325-G004 acts as a strong gravitational lens, distorting light from a distant galaxy behind it to create an Einstein 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.[141][142]

See also

References

Notes

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