Editing General relativity (section)

== Astrophysical applications ==
=== Gravitational lensing ===
{{Main|Gravitational lensing}}
[[File:Einstein cross (cropped).jpg|thumb|upright=0.88|[[Einstein cross]]: four images of the same astronomical object, produced by a gravitational lens]]
The deflection of light by gravity is responsible for a new class of astronomical phenomena. If a massive object is situated between the astronomer and a distant target object with appropriate mass and relative distances, the astronomer will see multiple distorted images of the target. Such effects are known as gravitational lensing.<ref>For overviews of gravitational lensing and its applications, see {{Harvnb|Ehlers|Falco|Schneider|1992}} and {{Harvnb|Wambsganss|1998}}</ref> Depending on the configuration, scale, and mass distribution, there can be two or more images, a bright ring known as an [[Einstein ring]], or partial rings called arcs.<ref>For a simple derivation, see {{Harvnb|Schutz|2003|loc=ch. 23}}; cf. {{Harvnb|Narayan|Bartelmann|1997|loc=sec. 3}}</ref>
The [[Twin Quasar|earliest example]] was discovered in 1979;<ref>{{Harvnb|Walsh|Carswell|Weymann|1979}}</ref> since then, more than a hundred gravitational lenses have been observed.<ref>Images of all the known lenses can be found on the pages of the CASTLES project, {{Harvnb|Kochanek|Falco|Impey|Lehar|2007}}</ref> Even if the multiple images are too close to each other to be resolved, the effect can still be measured, e.g., as an overall brightening of the target object; a number of such "[[microlensing]] events" have been observed.<ref>{{Harvnb|Roulet|Mollerach|1997}}</ref>

Gravitational lensing has developed into a tool of [[observational astronomy]]. It is used to detect the presence and distribution of [[dark matter]], provide a "natural telescope" for observing distant galaxies, and to obtain an independent estimate of the [[Hubble constant]]. Statistical evaluations of lensing data provide valuable insight into the structural evolution of [[galaxy|galaxies]].<ref>{{Harvnb|Narayan|Bartelmann|1997|loc=sec. 3.7}}</ref>

=== Gravitational-wave astronomy ===
{{Main|Gravitational wave|Gravitational-wave astronomy}}
[[File:LISA.jpg|thumb|upright=0.8|Artist's impression of the space-borne gravitational wave detector [[Laser Interferometer Space Antenna|LISA]]]]
Observations of binary pulsars provide strong indirect evidence for the existence of gravitational waves (see [[#Orbital decay|Orbital decay]], above). Detection of these waves is a major goal of current relativity-related research.<ref>{{Harvnb|Barish|2005}}, {{Harvnb|Bartusiak|2000}}, {{Harvnb|Blair|McNamara|1997}}</ref> Several land-based [[gravitational wave detector]]s are currently in operation, most notably the [[Interferometric gravitational wave detector|interferometric detectors]] [[GEO 600]], [[LIGO]] (two detectors), [[TAMA 300]] and [[Virgo interferometer|VIRGO]].<ref>{{Harvnb|Hough|Rowan|2000}}</ref> Various [[pulsar timing array]]s are using [[millisecond pulsar]]s to detect gravitational waves in the 10<sup>−9</sup> to 10<sup>−6</sup> [[hertz]] frequency range, which originate from binary supermassive blackholes.<ref>{{Citation | last1=Hobbs | first1=George |title=The international pulsar timing array project: using pulsars as a gravitational wave detector | last2=Archibald | first2=A. | last3=Arzoumanian | first3=Z. | last4=Backer | first4=D. | last5=Bailes | first5=M. | last6=Bhat | first6=N. D. R. | last7=Burgay | first7=M. | last8=Burke-Spolaor | first8=S. | last9=Champion | first9=D. | display-authors = 8| doi=10.1088/0264-9381/27/8/084013 | date=2010 | journal=Classical and Quantum Gravity | volume=27 | issue=8 | page=084013 |arxiv=0911.5206 |bibcode = 2010CQGra..27h4013H | s2cid=56073764 }}</ref> A European space-based detector, [[Laser Interferometer Space Antenna|eLISA / NGO]], is currently under development,<ref>{{Harvnb|Danzmann|Rüdiger|2003}}</ref> with a precursor mission ([[LISA Pathfinder]]) having launched in December 2015.<ref>{{cite web|url=http://www.esa.int/esaSC/120397_index_0_m.html|title=LISA pathfinder overview|publisher=ESA|access-date=23 April 2012}}</ref>

Observations of gravitational waves promise to complement observations in the [[electromagnetic spectrum]].<ref>{{Harvnb|Thorne|1995}}</ref> They are expected to yield information about black holes and other dense objects such as neutron stars and white dwarfs, about certain kinds of [[supernova]] implosions, and about processes in the very early universe, including the signature of certain types of hypothetical [[cosmic string]].<ref>{{Harvnb|Cutler|Thorne|2002}}</ref> In February 2016, the Advanced LIGO team announced that they had detected gravitational waves from a black hole merger.<ref name="Discovery 2016" /><ref name="Abbot" /><ref name="NSF" />

=== Black holes and other compact objects ===
{{Main|Black hole}}
[[File:Star collapse to black hole.png|thumb|left|Simulation based on the equations of general relativity: a star collapsing to form a black hole while emitting gravitational waves]]
Whenever the ratio of an object's mass to its radius becomes sufficiently large, general relativity predicts the formation of a black hole, a region of space from which nothing, not even light, can escape. In the currently accepted models of [[stellar evolution]], neutron stars of around 1.4 [[solar mass]]es, and stellar black holes with a few to a few dozen solar masses, are thought to be the final state for the evolution of massive stars.<ref>{{Harvnb|Miller|2002|loc=lectures 19 and 21}}</ref> Usually a galaxy has one [[supermassive black hole]] with a few million to a few [[1000000000 (number)|billion]] solar masses in its center,<ref>{{Harvnb|Celotti|Miller|Sciama|1999|loc=sec. 3}}</ref> and its presence is thought to have played an important role in the formation of the galaxy and larger cosmic structures.<ref>{{Harvnb|Springel|White|Jenkins|Frenk|2005}} and the accompanying summary {{Harvnb|Gnedin|2005}}</ref>

Astronomically, the most important property of compact objects is that they provide a supremely efficient mechanism for converting gravitational energy into electromagnetic radiation.<ref>{{Harvnb|Blandford|1987|loc=sec. 8.2.4}}</ref> [[Accretion (astrophysics)|Accretion]], the falling of dust or gaseous matter onto stellar or supermassive black holes, is thought to be responsible for some spectacularly luminous astronomical objects, notably diverse kinds of active galactic nuclei on galactic scales and stellar-size objects such as microquasars.<ref>For the basic mechanism, see {{Harvnb|Carroll|Ostlie|1996|loc=sec. 17.2}}; for more about the different types of astronomical objects associated with this, cf. {{Harvnb|Robson|1996}}</ref> In particular, accretion can lead to [[relativistic jet]]s, focused beams of highly energetic particles that are being flung into space at almost light speed.<ref>For a review, see {{Harvnb|Begelman|Blandford|Rees|1984}}. To a distant observer, some of these jets even appear to move [[superluminal motion|faster than light]]; this, however, can be explained as an optical illusion that does not violate the tenets of relativity, see {{Harvnb|Rees|1966}}</ref>
General relativity plays a central role in modelling all these phenomena,<ref>For stellar end states, cf. {{Harvnb|Oppenheimer|Snyder|1939}} or, for more recent numerical work, {{Harvnb|Font|2003|loc=sec. 4.1}}; for supernovae, there are still major problems to be solved, cf. {{Harvnb|Buras|Rampp|Janka|Kifonidis|2003}}; for simulating accretion and the formation of jets, cf. {{Harvnb|Font|2003|loc=sec. 4.2}}. Also, relativistic lensing effects are thought to play a role for the signals received from [[X-ray pulsar]]s, cf. {{Harvnb|Kraus|1998}}</ref> and observations provide strong evidence for the existence of black holes with the properties predicted by the theory.<ref>The evidence includes limits on compactness from the observation of accretion-driven phenomena ("[[Eddington luminosity]]"), see {{Harvnb|Celotti|Miller|Sciama|1999}}, observations of stellar dynamics in the center of our own [[Milky Way]] galaxy, cf. {{Harvnb|Schödel|Ott|Genzel|Eckart|2003}}, and indications that at least some of the compact objects in question appear to have no solid surface, which can be deduced from the examination of [[X-ray burst]]s for which the central compact object is either a neutron star or a black hole; cf. {{Harvnb|Remillard|Lin|Cooper|Narayan|2006}} for an overview, {{Harvnb|Narayan|2006|loc=sec. 5}}. Observations of the "shadow" of the Milky Way galaxy's central black hole horizon are eagerly sought for, cf. {{Harvnb|Falcke|Melia|Agol|2000}}</ref>

Black holes are also sought-after targets in the search for gravitational waves (cf. [[#Gravitational waves|Gravitational waves]], above). Merging [[binary black hole|black hole binaries]] should lead to some of the strongest gravitational wave signals reaching detectors here on Earth, and the phase directly before the merger ("chirp") could be used as a "[[standard candle]]" to deduce the distance to the merger events–and hence serve as a probe of cosmic expansion at large distances.<ref>{{Harvnb|Dalal|Holz|Hughes|Jain|2006}}</ref> The gravitational waves produced as a stellar black hole plunges into a supermassive one should provide direct information about the supermassive black hole's geometry.<ref>{{Harvnb|Barack|Cutler|2004}}</ref>

=== Cosmology ===
{{Main|Physical cosmology}}
[[File:Lensshoe hubble.jpg|thumb|This blue horseshoe is a distant galaxy that has been magnified and warped into a nearly complete ring by the strong gravitational pull of the massive foreground luminous red galaxy.]]
The current models of cosmology are based on [[Einstein's field equations]], which include the cosmological constant <math>\Lambda</math> since it has important influence on the large-scale dynamics of the cosmos,
:<math> R_{\mu\nu} - {\textstyle 1 \over 2}R\,g_{\mu\nu} + \Lambda\ g_{\mu\nu} = \frac{8\pi G}{c^{4}}\, T_{\mu\nu} </math>
where ''<math>g_{\mu\nu}</math>'' is the spacetime metric.<ref>{{Harvnb|Einstein|1917}}; cf. {{Harvnb|Pais|1982|pp=285–288}}</ref> [[Isotropic]] and homogeneous solutions of these enhanced equations, the [[Friedmann–Lemaître–Robertson–Walker metric|Friedmann–Lemaître–Robertson–Walker solutions]],<ref>{{Harvnb|Carroll|2001|loc=ch. 2}}</ref> allow physicists to model a universe that has evolved over the past 14&nbsp;[[1000000000 (number)|billion]]&nbsp;years from a hot, early Big Bang phase.<ref>{{Harvnb|Bergström|Goobar|2003|loc=ch. 9–11}}; use of these models is justified by the fact that, at large scales of around hundred million [[light-year]]s and more, our own universe indeed appears to be isotropic and homogeneous, cf. {{Harvnb|Peebles|Schramm|Turner|Kron|1991}}</ref> Once a small number of parameters (for example the universe's mean matter density) have been fixed by astronomical observation,<ref>E.g. with [[WMAP]] data, see {{Harvnb|Spergel|Verde|Peiris|Komatsu|2003}}</ref> further observational data can be used to put the models to the test.<ref>These tests involve the separate observations detailed further on, see, e.g., fig. 2 in {{Harvnb|Bridle|Lahav|Ostriker|Steinhardt|2003}}</ref> Predictions, all successful, include the initial abundance of chemical elements formed in a period of [[Big Bang nucleosynthesis|primordial nucleosynthesis]],<ref>{{Harvnb|Peebles|1966}}; for a recent account of predictions, see {{Harvnb|Coc, Vangioni‐Flam et al.|2004}}; an accessible account can be found in {{Harvnb|Weiss|2006}}; compare with the observations in {{Harvnb|Olive|Skillman|2004}}, {{Harvnb|Bania|Rood|Balser|2002}}, {{Harvnb|O'Meara|Tytler|Kirkman|Suzuki|2001}}, and {{Harvnb|Charbonnel|Primas|2005}}</ref> the large-scale structure of the universe,<ref>{{Harvnb|Lahav|Suto|2004}}, {{Harvnb|Bertschinger|1998}}, {{Harvnb|Springel|White|Jenkins|Frenk|2005}}</ref> and the existence and properties of a "[[thermal radiation|thermal]] echo" from the early cosmos, the [[cosmic background radiation]].<ref>{{Harvnb|Alpher|Herman|1948}}, for a pedagogical introduction, see {{Harvnb|Bergström|Goobar|2003|loc=ch. 11}}; for the initial detection, see {{Harvnb|Penzias|Wilson|1965}} and, for precision measurements by satellite observatories, {{Harvnb|Mather|Cheng|Cottingham|Eplee|1994}} ([[Cosmic Background Explorer|COBE]]) and {{Harvnb|Bennett|Halpern|Hinshaw|Jarosik|2003}} (WMAP). Future measurements could also reveal evidence about gravitational waves in the early universe; this additional information is contained in the background radiation's [[polarized light|polarization]], cf. {{Harvnb|Kamionkowski|Kosowsky|Stebbins|1997}} and {{Harvnb|Seljak|Zaldarriaga|1997}}</ref>

Astronomical observations of the cosmological expansion rate allow the total amount of matter in the universe to be estimated, although the nature of that matter remains mysterious in part. About 90% of all matter appears to be dark matter, which has mass (or, equivalently, gravitational influence), but does not interact electromagnetically and, hence, cannot be observed directly.<ref>Evidence for this comes from the determination of cosmological parameters and additional observations involving the dynamics of galaxies and galaxy clusters cf. {{Harvnb|Peebles|1993|loc=ch. 18}}, evidence from gravitational lensing, cf. {{Harvnb|Peacock|1999|loc=sec. 4.6}}, and simulations of large-scale structure formation, see {{Harvnb|Springel|White|Jenkins|Frenk|2005}}</ref> There is no generally accepted description of this new kind of matter, within the framework of known [[particle physics]]<ref>{{Harvnb|Peacock|1999|loc=ch. 12}}, {{Harvnb|Peskin|2007}}; in particular, observations indicate that all but a negligible portion of that matter is not in the form of the usual [[elementary particle]]s ("non-[[baryon]]ic matter"), cf. {{Harvnb|Peacock|1999|loc=ch. 12}}</ref> or otherwise.<ref>Namely, some physicists have questioned whether or not the evidence for dark matter is, in fact, evidence for deviations from the Einsteinian (and the Newtonian) description of gravity cf. the overview in {{Harvnb|Mannheim|2006|loc=sec. 9}}</ref> Observational evidence from redshift surveys of distant supernovae and measurements of the cosmic background radiation also show that the evolution of our universe is significantly influenced by a cosmological constant resulting in an acceleration of cosmic expansion or, equivalently, by a form of energy with an unusual [[equation of state]], known as [[dark energy]], the nature of which remains unclear.<ref>{{Harvnb|Carroll|2001}}; an accessible overview is given in {{Harvnb|Caldwell|2004}}. Here, too, scientists have argued that the evidence indicates not a new form of energy, but the need for modifications in our cosmological models, cf. {{Harvnb|Mannheim|2006|loc=sec. 10}}; aforementioned modifications need not be modifications of general relativity, they could, for example, be modifications in the way we treat the inhomogeneities in the universe, cf. {{Harvnb|Buchert|2008}}</ref>

An [[cosmic inflation|inflationary phase]],<ref>A good introduction is {{Harvnb|Linde|2005}}; for a more recent review, see {{Harvnb|Linde|2006}}</ref> an additional phase of strongly accelerated expansion at cosmic times of around 10<sup>−33</sup> seconds, was hypothesized in 1980 to account for several puzzling observations that were unexplained by classical cosmological models, such as the nearly perfect homogeneity of the cosmic background radiation.<ref>More precisely, these are the [[flatness problem]], the [[horizon problem]], and the [[monopole problem]]; a pedagogical introduction can be found in {{Harvnb|Narlikar|1993|loc=sec. 6.4}}, see also {{Harvnb|Börner|1993|loc=sec. 9.1}}</ref> Recent measurements of the cosmic background radiation have resulted in the first evidence for this scenario.<ref>{{Harvnb|Spergel|Bean|Doré|Nolta|2007|loc=sec. 5,6}}</ref> However, there is a bewildering variety of possible inflationary scenarios, which cannot be restricted by current observations.<ref>More concretely, the [[potential]] function that is crucial to determining the dynamics of the [[inflaton]] is simply postulated, but not derived from an underlying physical theory</ref> An even larger question is the physics of the earliest universe, prior to the inflationary phase and close to where the classical models predict the big bang [[Gravitational singularity|singularity]]. An authoritative answer would require a complete theory of quantum gravity, which has not yet been developed<ref>{{Harvnb|Brandenberger|2008|loc=sec. 2}}</ref> (cf. the section on [[#Quantum gravity|quantum gravity]], below).

=== Exotic solutions: time travel, warp drives ===
[[Kurt Gödel]] showed<ref>{{harvnb|Gödel|1949}}</ref> that solutions to Einstein's equations exist that contain [[closed timelike curve]]s (CTCs), which allow for loops in time. The solutions require extreme physical conditions unlikely ever to occur in practice, and it remains an open question whether further laws of physics will eliminate them completely. Since then, other—similarly impractical—GR solutions containing CTCs have been found, such as the [[Tipler cylinder]] and [[Wormhole#Traversable wormholes|traversable wormholes]]. [[Stephen Hawking]] introduced [[chronology protection conjecture]], which is an assumption beyond those of standard general relativity to prevent [[time travel]].

Some [[exact solutions in general relativity]] such as [[Alcubierre drive]] present examples of [[warp drive]] but these solutions requires exotic matter distribution, and generally suffers from semiclassical instability.
<ref>{{Cite journal
|last1=Finazzi|first1=Stefano
|last2= Liberati|first2=Stefano
|last3=Barceló|first3=Carlos
|date=15 June 2009
|title=Semiclassical instability of dynamical warp drives
|journal=Physical Review D
|language=en-US
|volume=79|issue=12|page=124017
|doi=10.1103/PhysRevD.79.124017
|arxiv=0904.0141
|bibcode=2009PhRvD..79l4017F
|s2cid=59575856
}}</ref>