Tests of general relativity serve to establish observational evidence for the
theory of general relativity. The first three tests, proposed by
Albert Einstein
Albert Einstein (14 March 187918 April 1955) was a German-born theoretical physicist who is best known for developing the theory of relativity. Einstein also made important contributions to quantum mechanics. His mass–energy equivalence f ...
in 1915, concerned the "anomalous"
precession
Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In o ...
of the
perihelion
An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. The line of apsides (also called apse line, or major axis of the orbit) is the line connecting the two extreme values.
Apsides perta ...
of
Mercury, the bending of light in
gravitational field
In physics, a gravitational field or gravitational acceleration field is a vector field used to explain the influences that a body extends into the space around itself. A gravitational field is used to explain gravitational phenomena, such as ...
s, and the
gravitational redshift
In physics and general relativity, gravitational redshift (known as Einstein shift in older literature) is the phenomenon that electromagnetic waves or photons travelling out of a gravitational well lose energy. This loss of energy correspo ...
. The precession of Mercury was already known; experiments showing light bending in accordance with the predictions of
general relativity
General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of grav ...
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
Irwin 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 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
Advanced LIGO team announced that they had
directly detected gravitational waves from a black hole merger.
This discovery, along with additional detections announced in June 2016 and June 2017,
[Conover, Emily]
LIGO snags another set of gravitational waves
''Science News'', June 1, 2017. Retrieved 8 June 2017. tested general relativity in the very strong field limit, observing to date no deviations from theory.
Classical tests
Albert Einstein
Albert Einstein (14 March 187918 April 1955) was a German-born theoretical physicist who is best known for developing the theory of relativity. Einstein also made important contributions to quantum mechanics. His mass–energy equivalence f ...
proposed
three tests of general relativity, subsequently called the "classical tests" of general relativity, in 1916:
# the perihelion precession of
Mercury's orbit
# the
deflection of light by the
Sun
# the
gravitational redshift
In physics and general relativity, gravitational redshift (known as Einstein shift in older literature) is the phenomenon that electromagnetic waves or photons travelling out of a gravitational well lose energy. This loss of energy correspo ...
of light
In the letter to ''
The Times
''The Times'' is a British Newspaper#Daily, daily Newspaper#National, national newspaper based in London. It began in 1785 under the title ''The Daily Universal Register'', adopting its modern name on 1 January 1788. ''The Times'' and its si ...
'' (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:
: "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

Under
Newtonian physics
Classical mechanics is a physical theory describing the motion of objects such as projectiles, parts of machinery, spacecraft, planets, stars, and galaxies. The development of classical mechanics involved substantial change in the methods ...
, an object in an (isolated) two-body system, consisting of the object orbiting a spherical mass, would trace out an
ellipse
In mathematics, an ellipse is a plane curve surrounding two focus (geometry), focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special ty ...
with the center of mass of the system at a
focus of the ellipse. The point of closest approach, called the
periapsis
An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. The line of apsides (also called apse line, or major axis of the orbit) is the line connecting the two extreme values.
Apsides perta ...
(or when the central body is the Sun,
perihelion
An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. The line of apsides (also called apse line, or major axis of the orbit) is the line connecting the two extreme values.
Apsides perta ...
), 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. The principal cause is the presence of other planets which
perturb one another's orbit. Another (much less significant) effect is solar
oblateness.
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 in
celestial mechanics
Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, to ...
, by
Urbain 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) per
tropical century (later re-estimated at 43″ by
Simon Newcomb
Simon Newcomb (March 12, 1835 – July 11, 1909) was a Canadians, Canadian–Americans, American astronomer, applied mathematician, and autodidactic polymath. He served as Professor of Mathematics in the United States Navy and at Johns Hopkins ...
in 1882).
[ A number of ''ad 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.] 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 named Vulcan. 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." Subsequently, no evidence of Vulcan was found and Einstein's 1915 general theory accounted for Mercury's anomalous precession. Einstein wrote to Michele Besso, "Perihelion motions explained quantitatively ... you will be astonished".
In general relativity, this remaining precession
Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In o ...
, 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 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 radar
Radar is a system that uses radio waves to determine the distance ('' ranging''), direction ( azimuth and elevation angles), and radial velocity of objects relative to the site. It is a radiodetermination method used to detect and track ...
. The total observed precession of Mercury is (574.10 ± 0.65)″ per century relative to the inertial ICRF. This precession can be attributed to the following causes:
The correction by ()″/cy is the prediction of post-Newtonian theory with parameters . 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:
:
where ''L'' is the semi-major axis
In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the two most widely separated points of the perimeter. The semi-major axis (major semiaxis) is the longe ...
, ''T'' is the orbital period
The orbital period (also revolution period) is the amount of time a given astronomical object takes to complete one orbit around another object. In astronomy, it usually applies to planets or asteroids orbiting the Sun, moons orbiting planets ...
, ''c'' is the speed of light, and ''e'' is the orbital eccentricity
In astrodynamics, the orbital eccentricity of an astronomical object is a dimensionless parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is a circular orbit, values be ...
(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 ()″/cy, Venus's is 8.62473″/cy and (8.6247 ± 0.0005)″/cy and Mars' is ()″/cy. Both values have now been measured, with results in good agreement with theory. The periapsis
An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. The line of apsides (also called apse line, or major axis of the orbit) is the line connecting the two extreme values.
Apsides perta ...
shift has also now been measured for binary pulsar systems, with PSR 1913+16 amounting to 4.2° per year. These observations are consistent with general relativity. 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,[Naeye, Robert]
"Stellar Mystery Solved, Einstein Safe"
''Sky and Telescope'', September 16, 2009. See als
MIT Press Release
September 17, 2009. Accessed 8 June 2017. have been measured as test cases for general relativity.
Deflection of light by the Sun
Henry Cavendish in 1784 (in an unpublished manuscript) and Johann Georg von Soldner in 1801 (published in 1804) had pointed out that Newtonian gravity predicts that starlight will bend around a massive object. 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: 1.75 arcsecond
A minute of arc, arcminute (abbreviated as arcmin), arc minute, or minute arc, denoted by the symbol , is a unit of angular measurement equal to of a degree. Since one degree is of a turn, or complete rotation, one arcminute is of a tu ...
s for light that grazes the Sun.
The first observation of light deflection was performed by noting the change in position of star
A star is a luminous spheroid of plasma (physics), plasma held together by Self-gravitation, self-gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night sk ...
s as they passed near the Sun on the celestial sphere
In astronomy and navigation, the celestial sphere is an abstract sphere that has an arbitrarily large radius and is concentric to Earth. All objects in the sky can be conceived as being projected upon the inner surface of the celestial sphere, ...
. The observations were performed by Arthur Eddington and his collaborators (see Eddington experiment) during the total solar eclipse of May 29, 1919, when the stars near the Sun (at that time in the constellation Taurus) could be observed. Observations were made simultaneously in the cities of Sobral, Ceará
Sobral is a municipality in the state of Ceará, Brazil.
Sobral is the fifth largest municipality of Ceará, after Fortaleza. Its economy is based on agriculture, services and some manufacturing industries. The city has two public universi ...
, Brazil and in São Tomé and Príncipe
São Tomé and Príncipe, officially the Democratic Republic of São Tomé and Príncipe, is an island country in the Gulf of Guinea, off the western equatorial coast of Central Africa. It consists of two archipelagos around the two main isla ...
on the west coast of Africa. 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."
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 to have been plagued by systematic error
Observational error (or measurement error) is the difference between a measurement, measured value of a physical quantity, quantity and its unknown true value.Dodge, Y. (2003) ''The Oxford Dictionary of Statistical Terms'', OUP. Such errors are ...
and possibly confirmation bias
Confirmation bias (also confirmatory bias, myside bias, or congeniality bias) is the tendency to search for, interpret, favor and recall information in a way that confirms or supports one's prior beliefs or Value (ethics and social sciences), val ...
, although modern reanalysis of the dataset suggests that Eddington's analysis was accurate.[D. Kennefick, "Testing relativity from the 1919 eclipse- a question of bias", ''Physics Today'', March 2009, pp. 37–42.] The measurement was repeated by a team from the Lick Observatory
The Lick Observatory is an astronomical observatory owned and operated by the University of California. It is on the summit of Mount Hamilton (California), Mount Hamilton, in the Diablo Range just east of San Jose, California, United States. The ...
led by the Director W. W. Campbell in the 1922 eclipse as observed in remote Australian station of Wallal, with results based on hundreds of star positions that agreed with the 1919 results and has been repeated several times since, most notably in 1953 by Yerkes Observatory astronomers and in 1973 by a team from the University of Texas
The University of Texas at Austin (UT Austin, UT, or Texas) is a public research university in Austin, Texas, United States. Founded in 1883, it is the flagship institution of the University of Texas System. With 53,082 students as of fall 2 ...
. Considerable uncertainty remained in these measurements for almost fifty years, until observations started being made at radio frequencies.
The deflection of starlight by the nearby white dwarf
A white dwarf is a Compact star, stellar core remnant composed mostly of electron-degenerate matter. A white dwarf is very density, dense: in an Earth sized volume, it packs a mass that is comparable to the Sun. No nuclear fusion takes place i ...
star Stein 2051 B has also been measured.
Gravitational redshift of light
Einstein predicted the gravitational redshift
In physics and general relativity, gravitational redshift (known as Einstein shift in older literature) is the phenomenon that electromagnetic waves or photons travelling out of a gravitational well lose energy. This loss of energy correspo ...
of light from the equivalence principle
The equivalence principle is the hypothesis that the observed equivalence of gravitational and inertial mass is a consequence of nature. The weak form, known for centuries, relates to masses of any composition in free fall taking the same t ...
in 1907, and it was predicted that this effect might be measured in the spectral lines of a white dwarf star, which has a very high gravitational field. Initial attempts to measure the gravitational redshift of the spectrum of 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.[Hetherington, N. S.]
"Sirius B and the gravitational redshift – an historical review"
''Quarterly Journal Royal Astronomical Society, vol. 21'', Sept. 1980, p. 246-252. Accessed 6 April 2017.[Holberg, J. B.]
''Journal for the History of Astronomy, Vol. 41,'' 1, 2010, p. 41-64. Accessed 6 April 2017. 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.
The redshift of Sirius B was finally measured by Greenstein ''et al.'' in 1971, obtaining the value for the gravitational redshift of , with more accurate measurements by the Hubble Space Telescope showing .
Tests of special relativity
The general theory of relativity incorporates Einstein's special theory of relativity, and hence tests of special relativity are also testing aspects of general relativity. As a consequence of the equivalence principle
The equivalence principle is the hypothesis that the observed equivalence of gravitational and inertial mass is a consequence of nature. The weak form, known for centuries, relates to masses of any composition in free fall taking the same t ...
, Lorentz invariance
In a relativistic theory of physics, a Lorentz scalar is a scalar expression whose value is invariant under any Lorentz transformation. A Lorentz scalar may be generated from, e.g., the scalar product of vectors, or by contracting tensors. While ...
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 Dicke and Schiff who laid out a framework for testing general relativity. 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; the parameterized post-Newtonian formalism in which deviations from general relativity can be quantified; and the framework of the equivalence principle
The equivalence principle is the hypothesis that the observed equivalence of gravitational and inertial mass is a consequence of nature. The weak form, known for centuries, relates to masses of any composition in free fall taking the same t ...
.
Experimentally, new developments in space exploration
Space exploration is the process of utilizing astronomy and space technology to investigate outer space. While the exploration of space is currently carried out mainly by astronomers with telescopes, its physical exploration is conducted bo ...
, electronics
Electronics is a scientific and engineering discipline that studies and applies the principles of physics to design, create, and operate devices that manipulate electrons and other Electric charge, electrically charged particles. It is a subfield ...
and condensed matter physics
Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid State of matter, phases, that arise from electromagnetic forces between atoms and elec ...
have made additional precise experiments possible, such as the Pound–Rebka experiment, laser interferometry and 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. This changed in 1960 with the introduction of Brans–Dicke theory which provided an alternative theory also in agreement with experimental observations. Ultimately, this led to the development of the parametrized post-Newtonian formalism by Nordtvedt and Will
Will may refer to:
Common meanings
* Will and testament, instructions for the disposition of one's property after death
* Will (philosophy), or willpower
* Will (sociology)
* Will, volition (psychology)
* Will, a modal verb - see Shall 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. The experiment is part of the Mercury Orbiter Radio science Experiment (MORE). 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 gravitational 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 distant radio sources. In particular, some quasar
A quasar ( ) is an extremely Luminosity, luminous active galactic nucleus (AGN). It is sometimes known as a quasi-stellar object, abbreviated QSO. The emission from an AGN is powered by accretion onto a supermassive black hole with a mass rangi ...
s 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 called very 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. 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's nutation, rotation, atmospheric refraction, tectonic displacement and tidal waves. Another important effect is refraction of the radio waves by the solar corona
In astronomy, a corona (: coronas or coronae) is the outermost layer of a star's Stellar atmosphere, atmosphere. It is a hot but relatively luminosity, dim region of Plasma (physics), plasma populated by intermittent coronal structures such as so ...
. Fortunately, this effect has a characteristic spectrum
A spectrum (: spectra or spectrums) is a set of related ideas, objects, or properties whose features overlap such that they blend to form a continuum. The word ''spectrum'' was first used scientifically in optics to describe the rainbow of co ...
, 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
The European Space Agency (ESA) is a 23-member International organization, international organization devoted to space exploration. With its headquarters in Paris and a staff of around 2,547 people globally as of 2023, ESA was founded in 1975 ...
astrometric satellite Hipparcos
''Hipparcos'' was a scientific satellite of the European Space Agency (ESA), launched in 1989 and operated until 1993. It was the first space experiment devoted to precision astrometry, the accurate measurement of the positions and distances of ...
. It measured the positions of about 105 stars. During the full mission about 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 star
A star is a luminous spheroid of plasma (physics), plasma held together by Self-gravitation, self-gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night sk ...
s in the Milky Way
The Milky Way or Milky Way Galaxy is the galaxy that includes the Solar System, with the name describing the #Appearance, galaxy's appearance from Earth: a hazy band of light seen in the night sky formed from stars in other arms of the galax ...
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.
Light travel time delay testing
Irwin I. Shapiro
Irwin Ira Shapiro is an American astrophysicist and Harvard University Professor, Timken University Professor at Harvard University. He has been a professor at Harvard since 1982.
He was the director of the Harvard-Smithsonian Center for Astr ...
proposed another test, beyond the classical tests, which could be performed within the Solar System. It is sometimes called the fourth "classical" test of general relativity
General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of grav ...
. He predicted a relativistic time delay ( Shapiro delay) in the round-trip travel time for radar signals reflecting off other planets. The mere curvature of the path of a photon
A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless particles that can ...
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
Time dilation is the difference in elapsed time as measured by two clocks, either because of a relative velocity between them (special relativity), or a difference in gravitational potential between their locations (general relativity). When unsp ...
in the gravitational potential
In classical mechanics, the gravitational potential is a scalar potential associating with each point in space the work (energy transferred) per unit mass that would be needed to move an object to that point from a fixed reference point in the ...
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.
More recently, the Cassini probe has undertaken a similar experiment which gave agreement with general relativity at the 0.002% level. However, the following detailed studies revealed that the measured value of the PPN parameter gamma is affected by a gravitomagnetic effect caused by the orbital motion of Sun around 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 and Saturn.
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 tidal forces
The tidal force or tide-generating force is the difference in gravitational attraction between different points in a gravitational field, causing bodies to be pulled unevenly and as a result are being stretched towards the attraction. It is the d ...
. This idea has been tested to extremely high precision by Eötvös 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 gravitational Yukawa interaction
In particle physics, Yukawa's interaction or Yukawa coupling, named after Hideki Yukawa, is an interaction between particles according to the Yukawa potential. Specifically, it is between a scalar field (or pseudoscalar field) \ \phi\ and a Dira ...
are very strong, and are discussed under fifth force and weak equivalence principle.
A version of the equivalence principle, called the strong 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 the Nordtvedt effect and is most precisely tested by the Lunar Laser Ranging Experiment
Lunar Laser Ranging (LLR) is the practice of measuring Lunar distance (astronomy), the distance between the surfaces of the Earth and the Moon using Lidar, laser ranging. The distance can be calculated from the Round-trip delay, round-trip time ...
. Since 1969, it has continuously measured the distance from several rangefinding stations on Earth to reflectors on the Moon to approximately centimeter accuracy. 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 gravitational constant
The gravitational constant is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's general relativity, theory of general relativity. It ...
, 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 the Einstein equivalence principle section of the equivalence principle article.
Gravitational redshift and time dilation
The first of the classical tests discussed above, the gravitational redshift
In physics and general relativity, gravitational redshift (known as Einstein shift in older literature) is the phenomenon that electromagnetic waves or photons travelling out of a gravitational well lose energy. This loss of energy correspo ...
, is a simple consequence of 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
A white dwarf is a Compact star, stellar core remnant composed mostly of electron-degenerate matter. A white dwarf is very density, dense: in an Earth sized volume, it packs a mass that is comparable to the Sun. No nuclear fusion takes place i ...
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
Time dilation is the difference in elapsed time as measured by two clocks, either because of a relative velocity between them (special relativity), or a difference in gravitational potential between their locations (general relativity). When unsp ...
) 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. 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.
The blueshift of a falling photon can be found by assuming it has an equivalent mass based on its frequency (where ''h'' is the Planck constant
The Planck constant, or Planck's constant, denoted by h, is a fundamental physical constant of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a ...
) along with , 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, where a hydrogen
Hydrogen is a chemical element; it has chemical symbol, symbol H and atomic number 1. It is the lightest and abundance of the chemical elements, most abundant chemical element in the universe, constituting about 75% of all baryon, normal matter ...
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
The Global Positioning System (GPS) is a satellite-based hyperbolic navigation system owned by the United States Space Force and operated by Mission Delta 31. It is one of the global navigation satellite systems (GNSS) that provide ge ...
(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.
Other precision tests of general relativity, 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.
Frame-dragging tests
Tests of the Lense–Thirring precession, consisting of small secular precession
Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In o ...
s 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 the LAGEOS satellites, but many aspects of them remain controversial. The same effect may have been detected in the data of the Mars Global Surveyor (MGS) spacecraft, a former probe in orbit around Mars
Mars is the fourth planet from the Sun. It is also known as the "Red Planet", because of its orange-red appearance. Mars is a desert-like rocky planet with a tenuous carbon dioxide () atmosphere. At the average surface level the atmosph ...
; also such a test raised a debate. First attempts to detect the Sun's Lense–Thirring effect on the perihelia of the inner planet
A planet is a large, Hydrostatic equilibrium, rounded Astronomical object, astronomical body that is generally required to be in orbit around a star, stellar remnant, or brown dwarf, and is not one itself. The Solar System has eight planets b ...
s have been recently reported as well. Frame dragging would cause the orbital plane of stars orbiting near a supermassive black hole
A supermassive black hole (SMBH or sometimes SBH) is the largest type of black hole, with its mass being on the order of hundreds of thousands, or millions to billions, of times the mass of the Sun (). Black holes are a class of astronomical ...
to precess about the black hole spin axis. This effect should be detectable within the next few years via astrometric
Astrometry is a branch of astronomy that involves precise measurements of the positions and movements of stars and other celestial bodies. It provides the kinematics and physical origin of the Solar System and this galaxy, the Milky Way.
History ...
monitoring of stars at the center of the Milky Way
The Milky Way or Milky Way Galaxy is the galaxy that includes the Solar System, with the name describing the #Appearance, galaxy's appearance from Earth: a hazy band of light seen in the night sky formed from stars in other arms of the galax ...
galaxy. 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.
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
Leland Stanford Junior University, commonly referred to as Stanford University, is a Private university, private research university in Stanford, California, United States. It was founded in 1885 by railroad magnate Leland Stanford (the eighth ...
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
''Physical Review Letters'' (''PRL''), established in 1958, is a peer-reviewed, scientific journal that is published 52 times per year by the American Physical Society. The journal is considered one of the most prestigious in the field of physics ...
'' 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. Investigator Francis Everitt explained that a milliarcsecond "is the width of a human hair seen at the distance of 10 miles".
In January 2012, LARES
Lares ( , ; archaic , singular ) were Tutelary deity#Ancient Rome, guardian deities in ancient Roman religion. Their origin is uncertain; they may have been hero-ancestors, guardians of the hearth, fields, boundaries, or fruitfulness, or an ama ...
satellite was launched on a Vega rocket to measure Lense–Thirring effect with an accuracy of about 1%, according to its proponents. This evaluation of the actual accuracy obtainable is a subject of debate.[
]
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 .
Mössbauer rotor experiment
It was conceived as a means to measure the time dilation
Time dilation is the difference in elapsed time as measured by two clocks, either because of a relative velocity between them (special relativity), or a difference in gravitational potential between their locations (general relativity). When unsp ...
effect on Earth after being motivated by Einstein's equivalence principle
The equivalence principle is the hypothesis that the observed equivalence of gravitational and inertial mass is a consequence of nature. The weak form, known for centuries, relates to masses of any composition in free fall taking the same t ...
that implies a rotating observer will be subject to the same transformations as an observer in a gravitational field. Mössbauer rotor experiments hence permit a precise terrestrial test of the relativistic Doppler effect. From a radioactive source fixed at the center of a spinning disc or rod, gamma rays
A gamma ray, also known as gamma radiation (symbol ), is a penetrating form of electromagnetic radiation arising from high energy interactions like the radioactive decay of atomic nuclei or astronomical events like solar flares. It consists o ...
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 the Clock hypothesis, Einstein's general relativity
General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of grav ...
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), Champeney ''et al.'' (1965), and Kündig (1963), 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, 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. This discovery was first explained as discrediting general relativity
General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of grav ...
and successfully confirming at the laboratory scale the predictions of an alternative theory of gravity developed by T. Yarman and his colleagues. 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'', which was unusually awarded a prize in 2018 by the Gravity Research Foundation for having secured ''a new proof of general relativity''. However, at the same time period, it was revealed that said author committed several mathematical errors in his calculations, and the supposed contribution of the so-called clock synchronization to the measured time dilation is in fact practically null. 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 black hole
A black hole is a massive, compact astronomical object so dense that its gravity prevents anything from escaping, even light. Albert Einstein's theory of general relativity predicts that a sufficiently compact mass will form a black hole. Th ...
s, especially those supermassive black hole
A supermassive black hole (SMBH or sometimes SBH) is the largest type of black hole, with its mass being on the order of hundreds of thousands, or millions to billions, of times the mass of the Sun (). Black holes are a class of astronomical ...
s which are thought to power active galactic nuclei and the more active quasar
A quasar ( ) is an extremely Luminosity, luminous active galactic nucleus (AGN). It is sometimes known as a quasi-stellar object, abbreviated QSO. The emission from an AGN is powered by accretion onto a supermassive black hole with a mass rangi ...
s, 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
Pulsars are rapidly rotating neutron star
A neutron star is the gravitationally collapsed Stellar core, core of a massive supergiant star. It results from the supernova explosion of a stellar evolution#Massive star, massive star—combined with gravitational collapse—that compresses ...
s 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 substantial periapsis
An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. The line of apsides (also called apse line, or major axis of the orbit) is the line connecting the two extreme values.
Apsides perta ...
precessions that cannot be accounted for classically but can be accounted for by using general relativity. For example, the Hulse–Taylor 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 quadrupole type or higher order vibration, or is asymmetric and in rotation, can emit gravitational waves. These gravitational waves are predicted to travel at the speed of light
The speed of light in vacuum, commonly denoted , is a universal physical constant exactly equal to ). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time i ...
. 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
Gravitational waves are oscillations of the gravitational field that travel through space at the speed of light; they are generated by the relative motion of gravitating masses. They were proposed by Oliver Heaviside in 1893 and then later by ...
).
The radiation of gravitational waves has been inferred from the Hulse–Taylor binary (and other binary pulsars). Precise timing of the pulses shows that the stars orbit only approximately according to Kepler's Laws
In astronomy, Kepler's laws of planetary motion, published by Johannes Kepler in 1609 (except the third law, which was fully published in 1619), describe the orbits of planets around the Sun. These laws replaced circular orbits and epicycles in ...
: over time they gradually spiral towards each other, demonstrating an energy
Energy () is the physical quantity, quantitative physical property, property that is transferred to a physical body, body or to a physical system, recognizable in the performance of Work (thermodynamics), work and in the form of heat and l ...
loss in close agreement with the predicted energy radiated by gravitational waves. For their discovery of the first binary pulsar and measuring its orbital decay due to gravitational-wave emission, Hulse and Taylor won the 1993 Nobel Prize in Physics
The Nobel Prize in Physics () is an annual award given by the Royal Swedish Academy of Sciences for those who have made the most outstanding contributions to mankind in the field of physics. It is one of the five Nobel Prizes established by the ...
.
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 star
A neutron star is the gravitationally collapsed Stellar core, core of a massive supergiant star. It results from the supernova explosion of a stellar evolution#Massive star, massive star—combined with gravitational collapse—that compresses ...
s 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% (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; but there are still some competing theories that would agree with these data.
Direct detection of gravitational waves
A number of gravitational-wave detectors have been built with the intent of directly detecting the gravitational waves emanating from such astronomical events as the merger of two neutron star
A neutron star is the gravitationally collapsed Stellar core, core of a massive supergiant star. It results from the supernova explosion of a stellar evolution#Massive star, massive star—combined with gravitational collapse—that compresses ...
s or black hole
A black hole is a massive, compact astronomical object so dense that its gravity prevents anything from escaping, even light. Albert Einstein's theory of general relativity predicts that a sufficiently compact mass will form a black hole. Th ...
s. In February 2016, the Advanced LIGO team announced that they had directly detected gravitational waves from a stellar binary black hole merger, with additional detections announced in June 2016, June 2017, and August 2017.
General relativity predicts gravitational waves, as does any theory of gravitation in which changes in the gravitational field propagate at a finite speed. Then, the LIGO response function could discriminate among the various theories. Since gravitational waves can be directly detected,[ 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 hole
A black hole is a massive, compact astronomical object so dense that its gravity prevents anything from escaping, even light. Albert Einstein's theory of general relativity predicts that a sufficiently compact mass will form a black hole. Th ...
s are the objects described by solutions of the Einstein field equations
In the General relativity, general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of Matter#In general relativity and cosmology, matter within it. ...
.
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.
"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.
Direct observation of black holes
The galaxy M87 was the subject of observation by the Event Horizon Telescope (EHT) in 2017; the 10 April 2019 issue of ''Astrophysical Journal Letters
''The Astrophysical Journal'' (''ApJ'') is a peer-reviewed scientific journal of astrophysics and astronomy, established in 1895 by American astronomers George Ellery Hale and James Edward Keeler. The journal discontinued its print edition and b ...
'' (vol. 875, No. 1) was dedicated to the EHT results, publishing six open-access
Open access (OA) is a set of principles and a range of practices through which nominally copyrightable publications are delivered to readers free of access charges or other barriers. With open access strictly defined (according to the 2001 de ...
papers. The event horizon
In astrophysics, an event horizon is a boundary beyond which events cannot affect an outside observer. Wolfgang Rindler coined the term in the 1950s.
In 1784, John Michell proposed that gravity can be strong enough in the vicinity of massive c ...
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.
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
The Very Large Telescope (VLT) is an astronomical facility operated since 1998 by the European Southern Observatory, located on Cerro Paranal in the Atacama Desert of northern Chile. It consists of four individual telescopes, each equipped with ...
using GRAVITY, NACO and SIFONI instruments. Additionally, there has now been detection of the Schwarzschild precession in the orbit of the star S2 near the Galactic centre massive black hole.
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
A neutron star is the gravitationally collapsed Stellar core, core of a massive supergiant star. It results from the supernova explosion of a stellar evolution#Massive star, massive star—combined with gravitational collapse—that compresses ...
in a 1.6-day orbit with a white dwarf
A white dwarf is a Compact star, stellar core remnant composed mostly of electron-degenerate matter. A white dwarf is very density, dense: in an Earth sized volume, it packs a mass that is comparable to the Sun. No nuclear fusion takes place i ...
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 (95% confidence level).
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
A black hole is a massive, compact astronomical object so dense that its gravity prevents anything from escaping, even light. Albert Einstein's theory of general relativity predicts that a sufficiently compact mass will form a black hole. Th ...
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, while the latter is much more promising. In both cases, systematic uncertainties might make such tests more challenging.
Cosmological tests
Tests of general relativity on the largest scales are not nearly so stringent as Solar System tests. The earliest such test was the prediction and discovery of the expansion of the universe
The expansion of the universe is the increase in proper length, distance between Gravitational binding energy, gravitationally unbound parts of the observable universe with time. It is an intrinsic and extrinsic properties (philosophy), intrins ...
.[ In 1922, Alexander Friedmann found that the Einstein equations have non-stationary solutions (even in the presence of the cosmological constant).][ 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).][ W.Pauli, 1958, pp. 219–220] Lemaître made an explicit prediction that the universe should expand.[ Kragh, 2003, p. 153] He also derived a redshift-distance relationship, which is now known as the Hubble Law. Later, in 1931, Einstein himself agreed with the results of Friedmann and Lemaître.[ The expansion of the universe discovered by ]Edwin Hubble
Edwin Powell Hubble (November 20, 1889 – September 28, 1953) was an American astronomer. He played a crucial role in establishing the fields of extragalactic astronomy and observational cosmology.
Hubble proved that many objects previously ...
in 1929[ was then considered by many (and continues to be considered by some now) as a direct confirmation of general relativity. In the 1930s, largely due to the work of 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.][ Rudnicki, 1991, p. 28. ''The Hubble Law was viewed by many as an observational confirmation of General Relativity in the early years''] However the prediction of a non-static universe was non-trivial, indeed dramatic, and primarily motivated by general relativity.
Some other cosmological tests include searches for primordial gravitational waves generated during cosmic inflation, which may be detected in the cosmic microwave background
The cosmic microwave background (CMB, CMBR), or relic radiation, is microwave radiation that fills all space in the observable universe. With a standard optical telescope, the background space between stars and galaxies is almost completely dar ...
polarization or by a proposed space-based gravitational-wave interferometer called the Big Bang Observer. Other tests at high redshift are constraints on other theories of gravity, and the variation of the gravitational constant since Big Bang nucleosynthesis
In physical cosmology, Big Bang nucleosynthesis (also known as primordial nucleosynthesis, and abbreviated as BBN) is a model for the production of light nuclei, deuterium, 3He, 4He, 7Li, between 0.01s and 200s in the lifetime of the universe ...
(it varied by no more than 40% since then).
In August 2017, the findings of tests conducted by astronomers using the European Southern Observatory
The European Organisation for Astronomical Research in the Southern Hemisphere, commonly referred to as the European Southern Observatory (ESO), is an intergovernmental organization, intergovernmental research organisation made up of 16 m ...
's Very Large Telescope
The Very Large Telescope (VLT) is an astronomical facility operated since 1998 by the European Southern Observatory, located on Cerro Paranal in the Atacama Desert of northern Chile. It consists of four individual telescopes, each equipped with ...
(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
''The Astrophysical Journal'' (''ApJ'') is a peer-reviewed scientific journal of astrophysics and astronomy, established in 1895 by American astronomers George Ellery Hale and James Edward Keeler. The journal discontinued its print edition and ...
''.
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.
See also
* General relativity
General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of grav ...
* Tests of special relativity
References
Notes
Other research papers
*
*
*
* A. Einstein, "Über das Relativitätsprinzip und die aus demselben gezogene Folgerungen", ''Jahrbuch der Radioaktivitaet und Elektronik'' 4 (1907); translated "On the relativity principle and the conclusions drawn from it", in ''The collected papers of Albert Einstein. Vol. 2 : The Swiss years: writings, 1900–1909'' (Princeton University Press, Princeton, New Jersey, 1989), Anna Beck translator. Einstein proposes the gravitational redshift of light in this paper, discussed online a
The Genesis of General Relativity
* A. Einstein, "Über den Einfluß der Schwerkraft auf die Ausbreitung des Lichtes", ''Annalen der Physik'' 35 (1911); translated "On the Influence of Gravitation on the Propagation of Light" in ''The collected papers of Albert Einstein. Vol. 3 : The Swiss years: writings, 1909–1911'' (Princeton University Press, Princeton, New Jersey, 1994), Anna Beck translator, and in ''The Principle of Relativity'', (Dover, 1924), pp 99–108, W. Perrett and G. B. Jeffery translators, . The deflection of light by the sun is predicted from the principle of equivalence. Einstein's result is half the full value found using the general theory of relativity.
*
* M. Froeschlé, F. Mignard and F. Arenou,
Determination of the PPN parameter γ with the Hipparcos data
Hipparcos Venice '97, ESA-SP-402 (1997).
*
*
*
*
Textbooks
* S. M. Carroll,
Spacetime and Geometry: an Introduction to General Relativity
', Addison-Wesley, 2003. A graduate-level general relativity textbook.
* A. S. Eddington,
Space, Time and Gravitation
', Cambridge University Press, reprint of 1920 ed.
* A. Gefter, "Putting Einstein to the Test", ''Sky and Telescope'' July 2005, p. 38. A popular discussion of tests of general relativity.
* H. Ohanian and R. Ruffini, ''Gravitation and Spacetime, 2nd Edition'' Norton, New York, 1994, . A general relativity textbook.
*
* C. M. Will, ''Theory and Experiment in Gravitational Physics'', Cambridge University Press, Cambridge (1993). A standard technical reference.
* C. M. Will, ''Was Einstein Right?: Putting General Relativity to the Test'', Basic Books (1993). This is a popular account of tests of general relativity.
Living Reviews papers
*
* An online, technical review, covering much of the material in ''Theory and experiment in gravitational physics.'' It is less comprehensive but more up to date.
External links
(for amount of observed and GR shifts).
{{DEFAULTSORT:Tests Of General Relativity
Mercury (planet)