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{{General relativity}}


At its introduction in 1915, the [[general relativity|general theory of relativity]] did not have a solid [[empirical evidence|empirical foundation]]. It was known that it correctly accounted for the "anomalous" [[precession]] of the [[perihelion]] of [[Mercury (planet)|Mercury]] and on philosophical grounds it was considered satisfying that it was able to unify [[Isaac Newton|Newton]]'s [[law of universal gravitation]] with [[special relativity]]. That light appeared to bend in gravitational fields in line with the predictions of general relativity was found in 1919 but it was not until a program of precision tests was started in 1959 that the various predictions of general relativity were tested to any further degree of accuracy in the weak gravitational field limit, severely limiting possible deviations from the theory. Beginning in 1974, [[Russell Alan Hulse|Hulse]], [[Joseph Hooton Taylor, Jr.|Taylor]] and others have studied the behaviour of [[binary pulsar]]s experiencing much stronger gravitational fields than found in our solar system. Both in the weak field limit (as in our solar system) and with the stronger fields present in systems of binary pulsars the predictions of general relativity have been extremely well tested locally.


The very strong gravitational fields that must be present close to [[black hole]]s, especially those [[supermassive black hole]]s which are thought to power [[active galactic nuclei]] and the more active [[quasar]]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 [[Alternatives to general relativity|theories of gravitation]], but they are qualitatively consistent with the black hole concept as modelled in general relativity.
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As a consequence of the [[equivalence principle]], [[Lorentz invariance]] holds locally in freely falling reference frames. Experiments related to Lorentz invariance and thus [[special relativity]] (i.e., when gravitational effects can be neglected) are described in [[Tests of special relativity]].
 
==Classical tests==
 
[[Albert Einstein]] proposed three tests of general relativity, subsequently called '''the classical tests of general relativity''', in 1916:<ref name = Ein1916>{{cite journal| last = Einstein| first = Albert| authorlink = Albert Einstein| co-authors = | title = The Foundation of the General Theory of Relativity| journal = Annalen der Physik| volume = 49 | issue = 7| pages = 769–822| year = 1916| publisher = | url = http://www.alberteinstein.info/gallery/gtext3.html| format = PDF | accessdate = 2006-09-03| doi = 10.1002/andp.19163540702 |bibcode = 1916AnP...354..769E }}</ref>
# the perihelion precession of [[Mercury (planet)|Mercury]]'s orbit
# the [[gravitational lens|deflection of light]] by the [[Sun]]
# the [[gravitational redshift]] of light
 
In the letter to the [[The Times|London Times]] 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:<ref>{{cite web|title=What Is The Theory Of Relativity?|author=Einstein, Albert (1919)|url=http://germanhistorydocs.ghi-dc.org/pdf/eng/EDU_Einstein_ENGLISH.pdf|publisher=German History in Documents and Images|format=PDF|accessdate=7 June 2013}}</ref>
{{Block quote|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===
[[File:Mercury transit 2.jpg|right|thumb|150px|Transit of Mercury on November 8, 2006 with [[sunspot]]s #921, 922, and 923]]
{{Details|Two-body problem in general relativity}}
 
Under Newtonian physics, a two-body system consisting of a lone object orbiting a spherical mass would trace out an [[ellipse]] with the spherical mass at a [[focus (geometry)|focus]]. The point of closest approach, called the [[periapsis]] (or, as the central body in our Solar System is the sun, [[perihelion]]), is fixed. A number of effects in our solar system cause the perihelia of planets to precess (rotate) around the sun. The principal cause is the presence of other planets which [[Perturbation (astronomy)|perturb]] each other's orbit. Another (much less significant) effect is solar [[oblate spheroid|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]], by [[Urbain Le Verrier]]. His re-analysis of available timed observations of transits of [[Mercury (planet)|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" (arc seconds) per tropical century (later re-estimated at 43").<ref>U. Le Verrier (1859), (in French), [http://www.archive.org/stream/comptesrendusheb49acad#page/378/mode/2up "Lettre de M. Le Verrier à M. Faye sur la théorie de Mercure et sur le mouvement du périhélie de cette planète"], Comptes rendus hebdomadaires des séances de l'Académie des sciences (Paris), vol. 49 (1859), pp.379–383.</ref> A number of ''ad hoc'' and ultimately unsuccessful solutions were proposed, but they tended to introduce more problems. In general relativity, this remaining [[Stellar precession|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<ref name = Ein1916/> 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 astronomy|radar]]. The total observed precession of Mercury is 574.10±0.65 [[arc-second]]s per century<ref name="Clemence">{{cite journal
| first=G. M. | last=Clemence
| title=The Relativity Effect in Planetary Motions
| journal=Reviews of Modern Physics | volume=19
| issue=4 | pages=361&ndash;364 | year=1947 |
doi=10.1103/RevModPhys.19.361 | bibcode=1947RvMP...19..361C}}</ref> relative to the inertial [[International Celestial Reference Frame|ICFR]]. This precession can be attributed to the following causes:
 
{| class="wikitable" style="margin-left:auto; margin-right:auto;"
|+'''Sources of the precession of perihelion for Mercury'''
|-
! Amount (arcsec/Julian century) !! Cause
|-
| 531.63 ±0.69<ref name="Clemence"/>
|| Gravitational tugs of the other planets
|-
| 0.0254 || Oblateness of the Sun ([[quadrupole moment]])
|-
| 42.98 ±0.04<ref>Myles Standish, Jet Propulsion Laboratory (1998) http://classroom.sdmesa.edu/ssiegel/Physics%20197/labs/Mercury%20Precession.pdf</ref> || General relativity
|-
| 574.64±0.69 || Total
|-
| 574.10±0.65<ref name="Clemence"/> || Observed
|}
 
The correction by 42.98" is 3/2 multiple of classical prediction with [[Parameterized post-Newtonian formalism|PPN parameters]] <math>\gamma=\beta=0</math>.<ref>http://www.tat.physik.uni-tuebingen.de/~kokkotas/Teaching/Experimental_Gravity_files/Hajime_PPN.pdf - Perihelion shift of Mercury, page 11</ref>
 
Thus the effect can be fully explained by general relativity. More recent calculations based on more precise measurements have not materially changed the situation.
 
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 of 3.84 seconds of arc per century, and Venus's is 8.62". Both values are in good agreement with observation.<ref name="Biswas">{{cite journal|version=v1|title=Relativistic perihelion precession of orbits of Venus and the Earth|first1=Abhijit|last1=Biswas|first2=Krishnan R. S.|last2= Mani|year=2008|doi=10.2478/s11534-008-0081-6|journal=Central European Journal of Physics|volume=6|issue=3|pages=754–758| arxiv=0802.0176|bibcode = 2008CEJPh...6..754B }}</ref> The [[periapsis]] shift of binary pulsar systems have been measured, with [[PSR 1913+16]] amounting to 4.2º per year.<ref name="Matzner">{{cite book |title=Dictionary of geophysics, astrophysics, and astronomy|first1=Richard Alfred|last1=Matzner|publisher=CRC Press|year=2001|isbn=0-8493-2891-8|page=356|url=http://books.google.com/books?id=eez38xjCYGkC&pg=PA356}}</ref> These observations are consistent with general relativity.<ref>{{cite conference |url=http://aspbooks.org/custom/publications/paper/328-0025.html |title=The Relativistic Binary Pulsar B1913+16: Thirty Years of Observations and Analysis |last1=Weisberg |first1=J.M. |last2=Taylor |first2=J.H. |authorlink2=Joseph Hooton Taylor, Jr. |date=July 2005 |publisher=[[Astronomical Society of the Pacific]] |location=[[San Francisco]] |booktitle=Binary Radio Pulsars |pages=25 |location=[[Aspen, Colorado]], [[USA]] |editor=F.A. Rasio and I.H. Stairs (eds.) |booktitle=ASP Conference Series |volume=328 |arxiv=astro-ph/0407149 |bibcode=2005ASPC..328...25W}}</ref> 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 - so a few systems such as [[DI Herculis]] have been considered as problematic cases for general relativity.
 
===Deflection of light by the Sun===
[[File:1919 eclipse negative.jpg|right|thumb|150px|One of [[Sir Arthur Eddington|Eddington]]'s photographs of the 1919 [[solar eclipse]] experiment, presented in his 1920 paper announcing its success]]
{{Details|Kepler problem in general relativity}}
 
[[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.<ref>{{Cite journal |last=Soldner, J. G. V. |year=1804 |title=[[s:On the Deflection of a Light Ray from its Rectilinear Motion|On the deflection of a light ray from its rectilinear motion, by the attraction of a celestial body at which it nearly passes by]] |journal=Berliner Astronomisches Jahrbuch |pages =161–172}}</ref> 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 (and thus Soldner's) 1911-result is only half of the correct value. Einstein became the first to calculate the correct value for light bending.<ref>{{Cite journal |last=Will, C.M.|year=2006 |title=The Confrontation between General Relativity and Experiment |journal=Living Rev. Relativity |volume =9 |url=http://www.livingreviews.org/lrr-2006-3 |page=39}}</ref>
 
The first observation of [[light]] deflection was performed by noting the change in position of [[star]]s as they passed near the Sun on the [[celestial sphere]]. The observations were performed in May 1919 by [[Sir Arthur Eddington|Arthur Eddington]] and his collaborators during a total [[solar eclipse]],<ref>{{cite journal| last = Dyson| first = F. W.| authorlink = | title = A determination of the deflection of light by the Sun's gravitational field, from observations made at the total eclipse of 29 May 1919| journal = Philosophical Transactions of the Royal Society | volume = 220A | issue = | pages = 291–333| year = 1920| publisher = | url = | accessdate =| coauthors = Eddington, A. S., Davidson C.}}</ref> so that the stars near the Sun could be observed. Observations were made simultaneously in the cities of [[Sobral, Ceará]], [[Brazil]] and in [[São Tomé and Príncipe]] on the west coast of Africa.<ref>{{cite journal| last = Stanley| first = Matthew| authorlink = | co-authors = | title = 'An Expedition to Heal the Wounds of War': The 1919 Eclipse and Eddington as Quaker Adventurer| journal = Isis | volume = 94| issue = 1| pages = 57–89| year = 2003| publisher = | url = | accessdate =| doi = 10.1086/376099| pmid = 12725104}}</ref> 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." <ref>Rosenthal-Schneider, Ilse: Reality and Scientific Truth. Detroit: Wayne State University Press, 1980. p 74. See also Calaprice, Alice: The New Quotable Einstein. Princeton: Princeton University Press, 2005. p 227.)</ref>
 
The early accuracy, however, was poor. The results were argued by some<ref>[[Harry Collins]] and [[Trevor Pinch]], ''The Golem'', ISBN 0-521-47736-0</ref> to have been plagued by [[systematic error]] and possibly [[confirmation bias]], although modern reanalysis of the dataset<ref>{{cite arXiv|eprint=0709.0685|author1=Daniel Kennefick|title=Not Only Because of Theory: Dyson, Eddington and the Competing Myths of  the 1919 Eclipse Expedition|class=physics.hist-ph|year=2007}}</ref> suggests that Eddington's analysis was accurate.<ref>{{cite journal|doi=10.1038/news070903-20|url=http://philipball.blogspot.com/2007/09/arthur-eddington-was-innocent-this-is.html|title=Arthur Eddington was innocent!|year=2007|last1=Ball|first1=Philip|journal=News@nature}}</ref><ref name="PhysToday">D. Kennefick, "Testing relativity from the 1919 eclipse- a question of bias," ''Physics Today,'' March 2009, pp. 37–42.</ref> The measurement was repeated by a team from the [[Lick Observatory]] in the 1922 eclipse, with results that agreed with the 1919 results<ref name="PhysToday" /> and has been repeated several times since, most notably in 1953 by [[Yerkes Observatory]] astronomers<ref>van Biesbroeck, G.: The relativity shift at the 1952 February 25 eclipse of the Sun., ''Astronomical Journal'', vol. 58, page 87, 1953.</ref> and in 1973 by a team from the [[University of Texas]].<ref>Texas Mauritanian Eclipse Team: Gravitational deflection of-light: solar eclipse of 30 June 1973 I. Description of procedures and final results., ''Astronomical Journal'', vol. 81, page 452, 1976.</ref> Considerable uncertainty remained in these measurements for almost fifty years, until observations started being made at [[radio astronomy|radio frequencies]]. It was not until the 1960s that it was definitively accepted that the amount of deflection was the full value predicted by general relativity, and not half that number.
The [[Einstein ring]] is an example of the deflection of light from distant galaxies by more nearby objects.
 
===Gravitational redshift of light===
[[File:Gravitational red-shifting2.png|thumb|150px|right|The gravitational redshift of a light wave as it moves upwards against a gravitational field (caused by the yellow star below).]]
Einstein predicted the [[gravitational redshift]] of light from the [[equivalence principle]] in 1907, but it is very difficult to measure astrophysically (see the discussion under ''Equivalence Principle'' below). Although it was measured by [[Walter Sydney Adams]] in 1925, it was only conclusively tested when the [[Pound–Rebka experiment]] in 1959 measured the relative redshift of two sources situated at the top and bottom of Harvard University's Jefferson tower using an extremely sensitive phenomenon called the [[Mössbauer effect]].<ref>{{cite journal|last=Pound| first=R. V. | authorlink = | date= November 1, 1959| title=Gravitational Red-Shift in Nuclear Resonance| journal=Physical Review Letters | volume = 3 | issue = 9 | pages=439–441 | doi=10.1103/PhysRevLett.3.439 | coauthors = Rebka Jr. G. A. | bibcode=1959PhRvL...3..439P}}</ref><ref>{{cite journal|last=Pound| first=R. V. | authorlink = | date= April 1, 1960| title=Apparent weight of photons| journal=Physical Review Letters| volume = 4 | issue = 7 | pages=337–341 | doi=10.1103/PhysRevLett.4.337 | coauthors = Rebka Jr. G. A. | bibcode=1960PhRvL...4..337P}}</ref> The result was in excellent agreement with general relativity. This was one of the first precision experiments testing general relativity.
 
==Modern tests==
The modern era of testing general relativity was ushered in largely at the impetus of [[Robert H. Dicke|Dicke]] and [[Leonard Isaac Schiff|Schiff]] who laid out a framework for testing general relativity.<ref>{{cite journal|last=Dicke| first= R. H. | authorlink = | date= March 6, 1959| title=New Research on Old Gravitation: Are the observed physical constants independent of the position, epoch, and velocity of the laboratory? | journal=Science| volume = 129 | issue = 3349 | pages=621–624 | doi=10.1126/science.129.3349.621| pmid=17735811|bibcode = 1959Sci...129..621D }}</ref><ref>{{cite conference| first = R. H. | last = Dicke| authorlink = | title = Mach's Principle and Equivalence| booktitle = Evidence for gravitational theories: proceedings of course 20 of the International School of Physics "Enrico Fermi" ed C. Møller | pages = | publisher = | year = 1962| location = | url = | doi = | accessdate = }}</ref><ref>{{cite journal|last=Schiff| first= L. I. | authorlink = Leonard Isaac Schiff | date= April 1, 1960| title=On Experimental Tests of the General Theory of Relativity| journal=American Journal of Physics| volume = 28 | issue = 4 | pages=340–343 | doi=10.1119/1.1935800|bibcode = 1960AmJPh..28..340S }}</ref> 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 [[alternatives to general relativity|alternative theories to general relativity]], in particular, [[scalar-tensor theory|scalar-tensor theories]] such as the [[Brans–Dicke theory]];<ref>{{cite journal|last=Brans| first= C. H.| authorlink = | date= November 1, 1961| title=Mach's Principle and a Relativistic Theory of Gravitation | journal=Physical Review| volume = 124 | issue = 3 | pages=925–935 | doi = 10.1103/PhysRev.124.925 | coauthors = Dicke, R. H.|bibcode = 1961PhRv..124..925B }}</ref> 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 [[space exploration]], [[electronics]] and [[condensed matter physics]] 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. Moreover, it is an extremely simple and elegant theory. This changed with the introduction of [[Brans–Dicke theory]] in 1960. This theory is arguably simpler, as it contains no [[dimensionless number|dimensionful]] constants, and is compatible with a version of [[Mach's principle]] and [[Paul Dirac|Dirac's]] [[Dirac large numbers hypothesis|large numbers hypothesis]], two philosophical ideas which have been influential in the history of relativity. Ultimately, this led to the development of the [[PPN formalism|parametrized post-Newtonian formalism]] by [[Kenneth Nordtvedt|Nordtvedt]] and [[Clifford Martin Will|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 <math>v/c</math>, 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 mission [[BepiColombo]] is testing the general relativity theory by measuring the parameters gamma and beta of the parametrized post-Newtonian formalism with high accuracy.<ref>[http://sci.esa.int/science-e/www/object/index.cfm?fobjectid=47346 Fact Sheet-BepiColombo]</ref>
 
===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 astronomy|radio sources]]. In particular, some [[quasar]]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 the Earth. The technique is called [[VLBI|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.<ref>{{cite journal | last=Fomalont |first= E.B.|authorlink = |date =July 2009|title= Progress in Measurements of the Gravitational Bending of Radio Waves Using the VLBA|journal=Astrophysical Journal |volume=699 |issue=2 |pages=1395–1402 |bibcode=2009ApJ...699.1395F | doi=10.1088/0004-637X/699/2/1395|coauthors = Kopeikin S.M.; Lanyi, G.; Benson, J.|arxiv = 0904.3992 }}</ref> 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 the Earth's [[nutation]], rotation, atmospheric refraction, tectonic displacement and tidal waves. Another important effect is refraction of the radio waves by the [[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 10<sup>5</sup> stars. During the full mission about {{val|3.5|e=6}} 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 mas, 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 mas. Systematic effects, however, limit the accuracy of the determination to 0.3% (Froeschlé, 1997).
 
In future, [[Gaia (spacecraft)|Gaia spacecraft]] will conduct a census of one billion [[star]]s in [[Milky Way|our Galaxy]] 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.<ref>[http://www.esa.int/export/esaSC/120377_index_0_m.html Gaia overview]</ref>
 
===Light travel time delay testing===
[[Irwin I. Shapiro]] proposed another test, beyond the classical tests, which could be performed within the solar system. It is sometimes called the fourth "classical" test of [[general relativity]]. He predicted a relativistic time delay ([[Shapiro delay]]) in the round-trip travel time for radar signals reflecting off other planets.<ref>{{cite journal | last=Shapiro | first= I. I. | authorlink = | date= December 28, 1964| title=Fourth test of general relativity| journal=Physical Review Letters| volume = 13 | issue = 26 | pages=789–791 | doi=10.1103/PhysRevLett.13.789 | bibcode=1964PhRvL..13..789S}}</ref> 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 which 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 it will be eclipsed by the Sun gives agreement with general relativity theory at the 5% level.<ref>{{cite journal | last=Shapiro | first= I. I. | authorlink = | date= May 3, 1971| title=Fourth Test of General Relativity: New Radar Result| journal=Physical Review Letters| volume = 26 | issue = 18 | pages=1132–1135 | doi=10.1103/PhysRevLett.26.1132 | coauthors = Ash M. E., Ingalls R. P., Smith W. B., Campbell D. B., Dyce R. B., Jurgens R. F. and Pettengill G. H. | bibcode=1971PhRvL..26.1132S}}</ref> More recently, the [[Cassini–Huygens|Cassini probe]] has undertaken a similar experiment which gave agreement with general relativity at the 0.002% level.<ref>{{cite journal|doi=10.1038/nature01997|title=A test of general relativity using radio links with the Cassini spacecraft|author= Bertotti B., Iess L., Tortora P.|journal=Nature|volume=425|issue=6956|pages= 374–376|year= 2003 |url=http://www.nature.com/nature/journal/v425/n6956/full/nature01997.html|pmid=14508481|bibcode=2003Natur.425..374B}}</ref> Very Long Baseline Interferometry has measured velocity-dependent (gravitomagnetic) corrections to the Shapiro time delay in the field of moving Jupiter <ref>{{cite journal | last=Fomalont |first= E.B.|authorlink = |date =November 2003|title= The Measurement of the Light Deflection from Jupiter: Experimental Results|journal=Astrophysical Journal|volume=598|issue=1|pages=704–711|bibcode=2003ApJ...598..704F | doi=10.1086/378785|coauthors = Kopeikin S.M.|arxiv = astro-ph/0302294 }}</ref><ref>{{cite journal | last=Kopeikin |first= S.M.|authorlink = |date =October 2007|title= Gravimagnetism, causality, and aberration of gravity in the gravitational light-ray deflection experiments|journal=General Relativity and Gravitation|volume=39|issue=10|pages=1583–1624 |bibcode=2007GReGr..39.1583K | doi=10.1007/s10714-007-0483-6 |coauthors = Fomalont E.B.|arxiv = gr-qc/0510077 }}</ref> and Saturn.<ref>{{cite journal | last=Fomalont |first= E.B.|authorlink = |date =January 2010|title= Recent VLBA/VERA/IVS tests of general relativity|journal=Proceedings of the International Astronomical Union, IAU Symposium|volume=261 | issue=S261 |pages=291–295 |bibcode=2010IAUS..261..291F | doi=10.1017/S1743921309990536 |coauthors = Kopeikin, S. M.; Jones, D.; Honma, M.; Titov, O.|arxiv = 0912.3421 }}</ref>
 
===The equivalence principle===
{{Main|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]]. This idea has been tested to incredible precision by [[Eötvös experiment|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]] 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]].<ref>{{cite journal | last=Nordtvedt Jr. | first= K. | authorlink = | date= May 25, 1968| title=Equivalence Principle for Massive Bodies. II. Theory | journal=Physical Review | volume = 169 | issue = 5 | pages=1017–1025 | doi = 10.1103/PhysRev.169.1017|bibcode = 1968PhRv..169.1017N }}</ref><ref>{{cite journal | last=Nordtvedt Jr. | first= K. | authorlink = | date= June 25, 1968| title=Testing Relativity with Laser Ranging to the Moon | journal=Physical Review | volume = 170 | issue = 5 | pages=1186–1187 | doi = 10.1103/PhysRev.170.1186 |bibcode = 1968PhRv..170.1186N }}</ref> Since 1969, it has continuously measured the distance from several rangefinding stations on Earth to reflectors on the Moon to approximately centimeter accuracy.<ref>{{cite journal | last=Williams | first= J. G. |authorlink = | date= December 29, 2004| title=Progress in Lunar Laser Ranging Tests of Relativistic Gravity | journal=Physical Review Letters| volume = 93 | issue = 5 | pages=1017–1025 | doi = 10.1103/PhysRevLett.93.261101 | coauthors = Turyshev, Slava G., Boggs, Dale H. | bibcode=2004PhRvL..93z1101W|arxiv = gr-qc/0411113 }}</ref> 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]],<ref>{{cite journal | last=Uzan | first= J. P. | authorlink = | year= 2003| title=The fundamental constants and their variation: Observational status and theoretical motivations | journal=Reviews of Modern Physics| volume = 75 | issue = 5 | pages=403– | arxiv= hep-ph/0205340| doi = 10.1103/RevModPhys.75.403| bibcode=2003RvMP...75..403U}}</ref> but one of the best comes from lunar rangefinding which suggests that the gravitational constant does not change by more than one part in 10<sup>11</sup> per year. The constancy of the other constants is discussed in the [[Einstein equivalence principle]] section of the equivalence principle article.
 
====Gravitational redshift====
The first of the classical tests discussed above, the [[gravitational redshift]], 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]] star [[Sirius]] B by Adams in 1925. Although this measurement, as well as later measurements of the spectral shift on other white dwarf stars, agreed with the prediction of relativity, it could be argued that the shift could possibly stem from some other cause, and hence 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 1960 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 experiment, performed by Pound and Rebka and later improved by Pound and Snyder, is called the [[Pound–Rebka experiment]]. The accuracy of the gamma-ray measurements was typically 1%. The blueshift of a falling photon can be found by assuming it has an equivalent mass based on its frequency <math>E=hf </math> (where ''h'' is [[Planck's constant]]) along with <math>E=mc^2</math>, 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,<ref>{{cite journal | last=Vessot | first= R. F. C.| authorlink = | date= December 29, 1980| title=Test of Relativistic Gravitation with a Space-Borne Hydrogen Maser | journal=Physical Review Letters | volume = 45 | issue = 26 | pages=2081–2084 | doi = 10.1103/PhysRevLett.45.2081 | coauthors = M. W. Levine, E. M. Mattison, E. L. Blomberg, T. E. Hoffman, G. U. Nystrom, B. F. Farrel, R. Decher, P. B. Eby, C. R. Baugher, J. W. Watts, D. L. Teuber and F. D. Wills | bibcode=1980PhRvL..45.2081V}}</ref> where a [[hydrogen]] [[maser]] clock on a rocket was launched to a height of 10,000&nbsp;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.
 
Other precision tests of general relativity,<ref>Gravitational Physics with Optical Clocks in Space - http://www.exphy.uni-duesseldorf.de/Opt_clocks_workshop/Talks_Workshop/Presentations%20Thursday%20morning/Presentation%20Schiller%20Gravitational%20Physics%20with%20Optical%20Clocks.pdf</ref> not discussed here,<!-- so far! --> 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; the [[Hafele–Keating experiment]], which used atomic clocks in circumnavigating aircraft to test general relativity and special relativity together;<ref>{{cite doi|10.1126/science.177.4044.166}}</ref><ref>{{cite doi|10.1126/science.177.4044.168}}</ref> and the forthcoming [[STEP (satellite)|Satellite Test of the Equivalence Principle]].
 
===Frame-dragging tests===
[[Image:LAGEOS-NASA.jpg|right|thumb|150px|The LAGEOS-1 satellite. ([[Diameter|D]]=60&nbsp;cm)]]
{{main|Frame-dragging}}
Tests of the [[Lense–Thirring precession]], consisting of small secular [[precession]]s of the orbit of a test particle in motion around a central rotating mass like, e.g., a planet or a star, have been performed with the [[LAGEOS]] satellites,<ref>{{cite journal | author = Ciufolini I. and Pavlis E.C.| title = A confirmation of the general relativistic prediction of the Lense–Thirring effect | journal = Nature |volume = 431 | year = 2004 |issue = 7011| pages = 958–960 | doi = 10.1038/nature03007 | pmid = 15496915 |bibcode = 2004Natur.431..958C }}</ref> but many aspects of them remain controversial.<ref>{{cite journal | authorlink= Lorenzo Iorio| author = Iorio L. | title = Conservative evaluation of the uncertainty in the LAGEOS-LAGEOS II Lense–Thirring test | journal = Central European Journal of Physics | year = 2009 |doi= 10.2478/s11534-009-0060-6 | volume= 8 | issue= 1 | page= 25|bibcode = 2010CEJPh...8...25I |arxiv = 0710.1022 }}</ref> The same effect may have been detected in the data of the [[Mars Global Surveyor]] (MGS) spacecraft,<ref>{{cite journal | authorlink= Lorenzo Iorio| author = Iorio L. | title = COMMENTS, REPLIES AND NOTES: A note on the evidence of the gravitomagnetic field of Mars | year = 2006 | journal = Classical Quantum Gravity | volume = 23| issue = 17| pages = 5451–5454 | doi = 10.1088/0264-9381/23/17/N01 |arxiv = gr-qc/0606092 |bibcode = 2006CQGra..23.5451I }}</ref> a former probe in orbit around [[Mars]]; also such a test raised a debate.<ref>{{cite journal | author = Krogh K. | title = Comment on 'Evidence of the gravitomagnetic field of Mars' | year = 2007 | journal = Classical Quantum Gravity | volume = 24 | issue = 22| pages = 5709–5715 | doi = 10.1088/0264-9381/24/22/N01 |bibcode = 2007CQGra..24.5709K }}</ref><ref>{{cite journal | authorlink= Lorenzo Iorio| author = Iorio L. | title = On the Lense–Thirring test with the Mars Global Surveyor in the gravitational field of Mars| journal = Central European Journal of Physics | year = 2009 | arxiv= gr-qc/0701146|bibcode = 2010CEJPh...8..509I |doi = 10.2478/s11534-009-0117-6 | volume= 8 | issue= 3 | pages= 509 }}</ref> First attempts to detect the [[Sun]]'s Lense–Thirring effect on the [[perihelia]] of the inner [[planet]]s have been recently reported<ref>{{cite journal | authorlink= Lorenzo Iorio| author = Iorio L. | title = Advances in the Measurement of the Lense–Thirring Effect with Planetary Motions in the Field of the Sun| journal = Scholarly Research Exchange | volume = 2008 | id = 105235| year = 2008 | doi = 10.3814/2008/105235 | page= 1|bibcode = 2008ScReE2008.5235I |arxiv = 0807.0435 }}</ref> 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 [[astrometry|astrometric]] monitoring of stars at the center of the [[Milky Way]] galaxy.<ref>{{Cite journal | last = Merritt | first = D. | last2 = Alexander | first2 = T. | last3 = Mikkola | first3 = S. | last4 = Will | first4 = C. | author-link = David Merritt | title = Testing Properties of the Galactic Center Black Hole Using Stellar Orbits | journal = Physical Review D | volume = 81 | issue = 6 | page = 062002 | year = 2010 | bibcode = 2010PhRvD..81f2002M | doi = 10.1103/PhysRevD.81.062002 | postscript = <!--None--> |arxiv = 0911.4718 }}</ref> By comparing the rate of orbital precession of two stars on different orbits, it is possible in principle to test the [[no-hair theorem]]s of general relativity.<ref>{{Cite journal | last = Will | first = C. | author-link = Clifford Will | title = Testing the General Relativistic "No-Hair" Theorems Using the Galactic Center Black Hole Sagittarius A* | journal = Astrophysical Journal Letters | volume = 674 | issue = 1 | pages = L25–L28 | date = | year = 2008 | doi = 10.1086/528847 | postscript = <!--None--> | bibcode=2008ApJ...674L..25W|arxiv = 0711.1677 }}</ref>
 
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 can be found. Principal investigators at [[Stanford University]] reported on May 4, 2011, that they had accurately measured the framing 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 the Earth's rotation) added up to 37 milliarcseconds with an error of about 19 percent.<ref name=Everitt>{{cite journal | author=Everitt | year=2011| title=Gravity Probe B: Final Results of a Space Experiment to Test General Relativity| journal=Physical Review Letters| volume = 106 | issue = 22 | pages=221101 | doi = 10.1103/PhysRevLett.106.221101 |arxiv =1105.3456 | bibcode=2011PhRvL.106v1101E | display-authors=1 | last2=Debra | first2=D. | last3=Parkinson | first3=B. | last4=Turneaure | first4=J. | last5=Conklin | first5=J. | last6=Heifetz | first6=M. | last7=Keiser | first7=G. | last8=Silbergleit | first8=A. | last9=Holmes | first9=T. | pmid=21702590}}</ref> Investigator Francis Everitt explained that a milliarcsecond "is the width of a human hair seen at the distance of 10 miles".<ref>{{cite web|author=Ker Than |url=http://news.nationalgeographic.com/news/2011/05/110505-einstein-theories-confirmed-gravity-probe-nasa-space-science/ |title=Einstein Theories Confirmed by NASA Gravity Probe |publisher=News.nationalgeographic.com |date= |accessdate=2011-05-08}}</ref>
 
In January 2012, [[LARES (satellite)|LARES]] satellite was launched on a [[Vega (rocket)|Vega]] rocket<ref>{{cite web
|url=http://www.spaceflightnow.com/vega/vv01/111207lares/
|title=Prepping satellite to test Albert Einstein
}}</ref> to measure [[Lense-Thirring effect]] with an accuracy of about 1%, according to its proponent.<ref>
{{cite journal
|last1=Ciufolini |first1=I.
|coauthors=''et al.''
|year=2009
|title=Towards a One Percent Measurement of Frame Dragging by Spin with Satellite Laser Ranging to LAGEOS, LAGEOS 2 and LARES and GRACE Gravity Models
|journal=[[Space Science Reviews]]
|volume=148 |pages=71–104
|arxiv=
|bibcode=2009SSRv..148...71C
|doi=10.1007/s11214-009-9585-7
}}</ref>
This evaluation of the actual accuracy obtainable is controversial.<ref>{{cite journal
|last1=Iorio |first1=L.
|year=2009
|title=Towards a 1% measurement of the Lense-Thirring effect with LARES?
|journal=[[Advances in Space Research]]
|volume=43 |issue=7 |pages=1148–1157
|arxiv= 0802.2031
|bibcode=2009AdSpR..43.1148I
|doi=10.1016/j.asr.2008.10.016
}}</ref><ref>
{{cite journal
|last1=Iorio |first1=L.
|year=2009
|title=Will the recently approved LARES mission be able to measure the Lense–Thirring effect at 1%?
|journal=[[General Relativity and Gravitation]]
|volume=41 |issue=8 |pages=1717–1724
|arxiv= 0803.3278
|bibcode=2009GReGr..41.1717I
|doi=10.1007/s10714-008-0742-1
}}</ref><ref>
{{cite journal
|last1=Iorio |first1=L.
|year=2009
|title=An Assessment of the Systematic Uncertainty in Present and Future Tests of the Lense-Thirring Effect with Satellite Laser Ranging
|journal=[[Space Science Reviews]]
|volume=148 |issue= |pages=363
|arxiv= 0809.1373
|bibcode=2009SSRv..148..363I
|doi=10.1007/s11214-008-9478-1
}}</ref><ref>
{{cite journal
|author1=Lorenzo Iorio
|title=Recent Attempts to Measure the General Relativistic Lense-Thirring Effect with Natural and Artificial Bodies in the Solar System
|year=2009
|volume=017
|journal=PoS ISFTG
|arxiv=0905.0300
|bibcode = 2009isft.confE..17I }}</ref><ref>
{{cite journal
|last1=Iorio |first1=L.
|journal=[[Acta Physica Polonica B]]
|year=2010
|title=On the impact of the atmospheric drag on the LARES mission
|url=http://th-www.if.uj.edu.pl/acta/vol41/pdf/v41p0753.pdf
|volume=41 |issue=4 |pages=753–765
|arxiv=
|bibcode=
|doi=
}}</ref><ref>
{{cite journal
|last1=Iorio |first1=L.
|last2=Lichtenegger |first2 = H.I.M.
|last3=Ruggiero |first3 = M.L.
|last4 = Corda |first4 = C.
|year=2011
|title=Phenomenology of the Lense-Thirring effect in the solar system
|journal=[[Astrophysics and Space Science]]
|volume=331 |issue=2 |pages=351
|arxiv=1009.3225
|bibcode=2011Ap&SS.331..351I
|doi=10.1007/s10509-010-0489-5
}}</ref><ref name="Ciufolini2009">
{{cite journal
|last1=Ciufolini |first1=I.
|coauthors=Paolozzi A., Pavlis E. C., Ries J. C., Koenig R., Matzner R. A., Sindoni G. and Neumayer H.
|year=2009
|title=Towards a One Percent Measurement of Frame Dragging by Spin with Satellite Laser Ranging to LAGEOS, LAGEOS 2 and LARES and GRACE Gravity Models
|journal=[[Space Science Reviews]]
|volume=148 |pages=71–104
|arxiv=
|bibcode=2009SSRv..148...71C
|doi=10.1007/s11214-009-9585-7
}}</ref><ref>
{{cite book
|last1=Ciufolini
|first1=I.
|coauthors=Paolozzi A., Pavlis E. C., Ries J. C., Koenig R., Matzner R. A., Sindoni G. and Neumayer H.
|title=[[General Relativity and John Archibald Wheeler]]
|chapter=Gravitomagnetism and Its Measurement with Laser Ranging to the LAGEOS Satellites and GRACE Earth Gravity Models
|pages=371–434
  |publisher=SpringerLink
|series=Astrophysics and Space Science Library
|volume=367
|year=2010
|doi=10.1007/978-90-481-3735-0_17
}}</ref><ref>
{{cite journal
| last1=Paolozzi
| first1=A.
| coauthors=Ciufolini I., Vendittozzi C.
| title=Engineering and scientific aspects of LARES satellite
| journal = Acta Astronautica
| volume = 69
| pages = 127–134
| year = 2011
| doi = 10.1016/j.actaastro.2011.03.005
| issn = 0094-5765
| issue = 3–4
}}</ref><ref>{{cite journal
| last1=Ciufolini
| first1=I.
| coauthors=Paolozzi A., Pavlis E. C., Ries J., Koenig R., Sindoni G., Neumeyer H.
| year=2011
| title=Testing Gravitational Physics with Satellite Laser Ranging
| journal=European Physical Journal Plus
| volume = 126
| page = 72
| doi = 10.1140/epjp/i2011-11072-2
| issue = 8
|bibcode = 2011EPJP..126...72C }}</ref><ref>{{cite journal
  | last = Ciufolini
  | first = I.
  | coauthors = Pavlis E. C., Paolozzi A., Ries J., Koenig R., Matzner R., Sindoni G., Neumayer K.H.
  | title = Phenomenology of the Lense-Thirring effect in the Solar System: Measurement of frame-dragging with laser ranged satellites
  | journal = New Astronomy
  | volume = 17
  | issue = 3
  | pages = 341–346
  | date = 2011-08-03
  | doi = 10.1016/j.newast.2011.08.003
  |bibcode = 2012NewA...17..341C }}</ref><ref>
{{cite journal
  | last = Ries
  | first = J.C.
  | coauthors = Ciufolini I., Pavlis E.C., Paolozzi A., Koenig R., Matzner R.A., Sindoni G., Neumayer H.
  | title = The Earth's frame-dragging via laser-ranged satellites: A Response to "Some considerations on the present-day results for the detection of frame-dragging after the final outcome of GP-B" by Iorio L
  | journal = Europhysics Letters
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  | issue = 3
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  | doi = 10.1209/0295-5075/96/30002
  | pages = 30002
  |bibcode = 2011EL.....9630002R }}</ref>
 
==Strong field tests: Binary pulsars==
{{further|Binary pulsar}}
 
[[File:Artist’s impression of the pulsar PSR J0348+0432 and its white dwarf companion.jpg|300px|thumb|Artist’s impression of the pulsar [[PSR J0348+0432]] and its white dwarf companion.<ref>{{cite news|title=Einstein Was Right — So Far|url=http://www.eso.org/public/news/eso1319/|accessdate=30 April 2013|newspaper=ESO Press Release}}</ref> ]]
 
[[Pulsars]] are rapidly rotating [[neutron star]]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]] 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&deg; of arc per year (periastron shift per orbit only about 10<sup>−6</sup>). 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.<ref>In general relativity, a perfectly spherical star (in vacuum) that expands or contracts while remaining perfectly spherical ''cannot'' emit any gravitational waves (similar to the lack of e/m radiation from a pulsating charge), as [[Birkhoff's theorem (relativity)|Birkhoff's theorem]] says that the geometry remains the same exterior to the star. More generally, a rotating system will only emit gravitational waves if it lacks the axial symmetry with respect to the axis of rotation.</ref> These [[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 (see [[gravitational waves]]) of gravitational radiation). Gravitational waves have been indirectly detected from the Hulse–Taylor binary. Precise timing of the pulses shows that the stars orbit only approximately according to [[Kepler's Laws]]: over time they gradually spiral towards each other, demonstrating an [[energy]] loss in close agreement with the predicted energy radiated by gravitational waves.<ref>{{cite journal | last=Weisberg | first= J. M. | date=  October 1981| title=Gravitational waves from an orbiting pulsar | journal=Scientific American | volume = 245 |  pages=74–82 | doi=10.1038/scientificamerican1081-74 | bibcode=1981SciAm.245...74W |  last2 = Taylor | first2 = J. H. | last3 = Fowler | first3 = L. A. }}</ref><ref>{{cite journal | last=Weisberg | first= J. M. | year=  2010| title=Timing Measurements of the Relativistic Binary Pulsar PSR B1913+16 | journal=Astrophysical Journal | volume = 722 |  pages=1030–1034 | doi=10.1088/0004-637X/722/2/1030 | arxiv =  1011.0718v1 | bibcode=2010ApJ...722.1030W
| last3 = Taylor | first3 = J. H. | last2 = Nice | first2 = D. J. }}</ref> Thus, although the waves have not been directly measured, their effect seems necessary to explain the orbits. For their discovery of this pulsar, [[Russell Alan Hulse|Hulse]] and [[Joseph Hooton Taylor, Jr.|Taylor]] won the [[Nobel prize]].
 
A "double pulsar" discovered in 2003, [[PSR J0737-3039]], has a periastron precession of 16.90&deg; 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%<ref>{{cite journal | author = Kramer, M. | title = Tests of general relativity from timing the double pulsar | journal = Science |volume = 314 | year = 2006 | pages = 97–102 | doi = 10.1126/science.1132305 | pmid = 16973838 | issue = 5796|arxiv = astro-ph/0609417 |bibcode = 2006Sci...314...97K | display-authors = 1 | last2 = Stairs | first2 = I. H. | last3 = Manchester | first3 = R. N. | last4 = McLaughlin | first4 = M. A. | last5 = Lyne | first5 = A. G. | last6 = Ferdman | first6 = R. D. | last7 = Burgay | first7 = M. | last8 = Lorimer | first8 = D. R. | last9 = Possenti | first9 = A. }}</ref> (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 report 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 8 millionths of a second per year, and confirmed GR predictions in a regime of extreme gravitational fields never probed before;<ref>{{cite journal | author =Antoniadis, John; et al |title=A Massive Pulsar in a Compact Relativistic Binary |url=http://www.sciencemag.org/content/340/6131/1233232.figures-only |doi=10.1126/science.1233232 |arxiv=astro-ph/1304.6875  |journal=Science |publisher=AAAS |volume=340 |issue=6131 |year=2013 |bibcode = 2013Sci...340..448A }}</ref> but there are still some competing theories that would agree with these data.<ref>{{cite web |url=http://www.nature.com/news/massive-double-star-is-latest-test-for-einstein-s-gravity-theory-1.12880#/b1 |title=Massive double star is latest test for Einstein’s gravity theory |publisher=Nature |date=25 April 2013 |work=Ron Cowen |accessdate=7 May 2013 }}</ref>
 
==Direct detection of gravitational waves==
 
As described immediately above in the [[#Strong field tests: Binary pulsars|Strong field tests: Binary pulsars]] section, binary pulsar observations have shown  conclusively although indirectly that  [[gravitational wave]]s exist.
A number of [[gravitational wave detector]]s have recently been built with the intent of ''directly'' detecting the [[gravitational wave]]s emanating from such astronomical events as the merger of two [[neutron star]]s. Currently, the most sensitive of these is the [[LIGO|Laser Interferometer Gravitational-wave Observatory (LIGO)]], which has been in operation since 2002. So far, there has not been a single detection event by any of the existing detectors. Future detectors are being developed or planned, which will greatly improve the sensitivity of these experiments, such as the Advanced LIGO detector being built for the LIGO facilities, and the proposed [[LISA (astronomy)|Laser Interferometer Space Antenna (LISA)]]. It is anticipated, for example, that Advanced LIGO will detect events possibly as often as daily.
 
General relativity predicts gravitational waves. These detectors have not yet found any gravitational waves. Continued failure to find waves as the detectors become more sensitive would tend to falsify general relativity. If, in the future, gravitational waves (of the predicted kind) were discovered, this would tend to confirm general relativity.
 
==Cosmological tests==
Tests of general relativity on the largest scales are not nearly so stringent as solar system tests.<ref>{{cite journal | author = Peebles, P. J. E.| authorlink = | date= December 2004| title=Testing general relativity on the scales of cosmology| arxiv= astro-ph/0410284|bibcode = 2005grg..conf..106P |doi = 10.1142/9789812701688_0010 | chapter = PROBING GENERAL RELATIVITY ON THE SCALES OF COSMOLOGY | isbn = 978-981-256-424-5 | pages = 106 }}</ref> The earliest such test was prediction and discovery of the [[expansion of the universe]].<ref name=Rudnicki28/> In 1922 [[Alexander Friedmann]] found that Einstein equations have non-stationary solutions (even in the presence of the [[cosmological constant]]).<ref name=Pauli1/><ref>[[#Kragh|Kragh]], 2003, p. 152</ref> 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).<ref name=Pauli1>[[#Pauli|W.Pauli]], 1958, pp.219–220</ref> Lemaître made an explicit prediction that the universe should expand.<ref name="Kragh, 2003, p. 153">[[#Kragh|Kragh]], 2003, p. 153</ref> He also derived a redshift-distance relationship, which is now known as the [[Hubble Law]].<ref name="Kragh, 2003, p. 153"/> Later, in 1931, Einstein himself agreed with the results of Friedmann and Lemaître.<ref name=Pauli1/> The expansion of the universe discovered by [[Edwin Hubble]] in 1929<ref name=Pauli1/> was then considered by many (and continues to be considered by some now) as a direct confirmation of general relativity.<ref>[[#Rudnicki|Rudnicki]], 1991, p. 28</ref> 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.<ref name=Rudnicki28>[[#Rudnicki|Rudnicki]], 1991, p. 28. ''The Hubble Law was viewed by many as an observational confirmation of General Relativity in the early years''</ref> However the prediction of a non-static universe was non-trivial, indeed dramatic, and primarily motivated by general relativity.<ref>[[#Chandrasekhar|Chandrasekhar]], 1980, p. 37</ref>
 
Some other cosmological tests include searches for primordial gravitational waves generated during [[cosmic inflation]], which may be detected in the [[cosmic microwave background]] [[Polarization (waves)|polarization]] or by a proposed space-based gravitational wave interferometer called [[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]] (it varied by no more than 40% since then){{citation needed|date=July 2012}}.
 
==See also==
*[[Tests of special relativity]]
*[[Cooperstock's Energy Localization Hypothesis]]
*[[Square Kilometre Array]]
 
==References==
 
===Notes===
 
{{Reflist|30em}}
 
===Other research papers===
{{refbegin}}
* {{cite journal | last1 = Bertotti | first1 = B. | last2 = Iess | first2 = L. | last3 = Tortora | first3 = P. | year = 2003 | title = A test of general relativity using radio links with the Cassini spacecraft | url = | journal = Nature | volume = 425 | issue = 6956|bibcode = 2003Natur.425..374B |doi = 10.1038/nature01997 | pmid=14508481 | pages = 374–6}}
* {{cite journal | last1 = Kopeikin | first1 = S. | last2 = Polnarev | first2 = A. | last3 = Schaefer | first3 = G. | last4 = Vlasov | first4 = I. | year = 2007 | title = Gravimagnetic effect of the barycentric motion of the Sun and determination of the post-Newtonian parameter γ in the Cassini experiment | url = | journal = Physics Letters A | volume = 367 | issue = 4–5| page = 276 | bibcode = 2007PhLA..367..276K|arxiv = gr-qc/0604060 |doi = 10.1016/j.physleta.2007.03.036 }}
* {{cite journal | doi = 10.1103/PhysRev.124.925 | last1 = Brans | first1 = C. | last2 = Dicke | first2 = R. H. | year = 1961 | title = Mach's principle and a relativistic theory of gravitation | url = | journal = Phys. Rev. | volume = 124 | issue = 3| pages = 925–35 |bibcode = 1961PhRv..124..925B }}
* 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, NJ, 1989), Anna Beck translator. Einstein proposes the gravitational redshift of light in this paper, discussed online at [http://www1.kcn.ne.jp/~h-uchii/gen.GR.html 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, NJ, 1994), Anna Beck translator, and in ''The Principle of Relativity,'' (Dover, 1924), pp 99–108, W. Perrett and G. B. Jeffery translators, ISBN 0-486-60081-5. 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.
*{{Cite journal | last = Shapiro | first = S. S. | authorlink = | title = Measurement of the solar gravitational deflection of radio waves using geodetic very-long-baseline interferometry data, 1979–1999 | journal = Physical Review Letters | volume = 92 | issue = 121101 | page = 121101| publisher = American Physical Society | date = 26 March 2004 | doi = 10.1103/PhysRevLett.92.121101 | coauthors = Davis, J. L.;Lebach, D. E.; Gregory J.S. | pmid=15089661 | bibcode=2004PhRvL..92l1101S}}
* M. Froeschlé, F. Mignard and F. Arenou, "[http://www.rssd.esa.int/Hipparcos/venice-proc/poster01_03.pdf Determination of the PPN parameter γ with the Hipparcos data]" Hipparcos Venice '97, ESA-SP-402 (1997).
* {{cite journal| author=Will, Clifford M. | title=Was Einstein Right? Testing Relativity at the Centenary| doi=10.1002/andp.200510170| year=2006| journal=Annalen der Physik| volume=15| pages=19–33 | arxiv=gr-qc/0504086|bibcode = 2006AnP...518...19W }}
* <span id="Rudnicki">{{cite journal|last=Rudnicki|first=Conrad|title=What are the Empirical Bases of the Hubble Law|year=1991|journal=Apeiron|pages=27–36|url=http://redshift.vif.com/JournalFiles/Pre2001/V0N09PDF/V0N09RUD.pdf|format=PDF|accessdate=2009-06-23|issue=9–10}}</span>
* <span id="Chandrasekhar">{{cite journal|last=Chandrasekhar|first=S.|title=The Role of General Relativity in Astronomy: Retrospect and Prospect|year=1980|journal=J. Astrophys. Astr.|volume=1|issue=1|pages=33–45|url=http://www.ias.ac.in/jarch/jaa/1/33-45.pdf|format=PDF|doi=10.1007/BF02727948|accessdate=2009-06-23|bibcode = 1980JApA....1...33C }}</span>
* <span id="Kragh">{{cite journal|last=Kragh|first=Helge|coauthors=Smith, Robert W.|title=Who discovered the expanding universe|year=2003|volume=41|pages=141–62|journal=History of Science|url=http://adsabs.harvard.edu/full/2003HisSc..41..141K|accessdate=2013-02-15|bibcode = 2003HisSc..41..141K|last2=Smith }}</span>
 
===Textbooks===
* S. M. Carroll, ''[http://pancake.uchicago.edu/~carroll/grbook/ Spacetime and Geometry: an Introduction to General Relativity]'', Addison-Wesley, 2003. An introductory general relativity textbook.
* A. S. Eddington, ''[http://books.google.com/books?id=7_U48JyJneQC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false Space, Time and Gravitation]'', Cambridge University Press, reprint of 1920 ed.
* A. Gefter, "Putting Einstein to the Test", ''Sky and Telescope'' July 2005, p.&nbsp;38. A popular discussion of tests of general relativity.
* H. Ohanian and R. Ruffini, ''Gravitation and Spacetime, 2nd Edition'' Norton, New York, 1994, ISBN 0-393-96501-5. A general relativity textbook.
* <span id="Pauli">{{cite book|last=Pauli|first=Wolfgang Ernst|title=Theory of Relativity|year=1958|isbn=978-0-486-64152-2|publisher=Courier Dover Publications|chapter=Part IV. General Theory of Relativity}}</span>
* 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.
* L. Iorio, ''[http://books.google.com/books?id=zeinb7OfDIUC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false The Measurement of Gravitomagnetism: A Challenging Enterprise]'', NOVA Science, Hauppauge (2007). It describes various theoretical and experimental/observational aspects of frame-dragging.
 
===Living Reviews papers===
* N. Ashby, [http://relativity.livingreviews.org/Articles/lrr-2003-1/ "Relativity in the Global Positioning System"], ''Living Reviews in Relativity'' (2003).
* C. M. Will, [http://www.livingreviews.org/lrr-2006-3 The Confrontation between General Relativity and Experiment], ''Living Reviews in Relativity'' (2006). 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.
{{refend}}
 
==External links==
* [http://www2.corepower.com:8080/~relfaq/experiments.html the USENET Relativity FAQ experiments page]
* [http://www.mathpages.com/rr/s6-02/6-02.htm Mathpages article on Mercury's perihelion shift] (for amount of observed and GR shifts).
<!-- POLICY NOTE: This is the main article for Category:Tests_of_general_relativity. Additional categorizations should be done for the category, not this article. -->
 
{{DEFAULTSORT:Tests Of General Relativity}}
[[Category:Tests of general relativity| ]]
[[Category:Mercury (planet)]]<!-- this category refers only to the perihelion precession of Mercury section, so despite the above note it should go in this article only -->

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