Editing General relativity (section)

== History ==
{{Main|History of general relativity|Classical theories of gravitation}}
[[Henri Poincaré]]'s 1905 theory of the dynamics of the electron was a relativistic theory which he applied to all forces, including gravity.  While others thought that gravity was instantaneous or of electromagnetic origin, he suggested that relativity was "something due to our methods of measurement". In his theory, he showed that [[gravitational waves]] propagate at the speed of light.<ref>{{Harvnb|Poincaré|1905}}</ref> Soon afterwards, Einstein started thinking about how to incorporate [[gravity]] into his relativistic framework. In 1907, beginning with a simple [[thought experiment]] involving an observer in free fall (FFO), he embarked on what would be an eight-year search for a relativistic theory of gravity. After numerous detours and false starts, his work culminated in the presentation to the [[Prussian Academy of Science]] in November 1915 of what are now known as the Einstein field equations, which form the core of Einstein's general theory of relativity.<ref>{{cite web|last1=O'Connor|first1=J.J.|last2=Robertson|first2=E.F.|date=May 1996|url= http://www-history.mcs.st-and.ac.uk/HistTopics/General_relativity.html|title=General relativity]}} {{Citation|url= http://www-history.mcs.st-and.ac.uk/Indexes/Math_Physics.html|title=History Topics: Mathematical Physics Index|archive-url= https://web.archive.org/web/20150204231934/http://www-history.mcs.st-and.ac.uk/Indexes/Math_Physics.html|archive-date=4 February 2015|publisher=School of Mathematics and Statistics, [[University of St. Andrews]]|location=Scotland|access-date=4 February 2015}}</ref> These equations specify how the geometry of space and time is influenced by whatever matter and radiation are present.<ref>{{Harvnb|Pais|1982|loc=ch. 9 to 15}}, {{Harvnb|Janssen|2005}}; an up-to-date collection of current research, including reprints of many of the original articles, is {{Harvnb|Renn|2007}}; an accessible overview can be found in {{Harvnb|Renn|2005|pp=110ff}}. Einstein's original papers are found in [http://einsteinpapers.press.princeton.edu/ Digital Einstein], volumes 4 and 6. An early key article is {{Harvnb|Einstein|1907}}, cf. {{Harvnb|Pais|1982|loc=ch. 9}}. The publication featuring the field equations is {{Harvnb|Einstein|1915}}, cf. {{Harvnb|Pais|1982|loc=ch. 11–15}}</ref> A version of [[non-Euclidean geometry]], called [[Riemannian geometry]], enabled Einstein to develop general relativity by providing the key mathematical framework on which he fit his physical ideas of gravity.<ref>Moshe Carmeli (2008).Relativity: Modern Large-Scale Structures of the Cosmos. pp.92, 93.World Scientific Publishing</ref> This idea was pointed out by mathematician [[Marcel Grossmann]] and published by Grossmann and Einstein in 1913.<ref>Grossmann for the mathematical part and Einstein for the physical part (1913). Entwurf einer verallgemeinerten Relativitätstheorie und einer Theorie der Gravitation (Outline of a Generalized Theory of Relativity and of a Theory of Gravitation), Zeitschrift für Mathematik und Physik, 62, 225–261. [http://www.pitt.edu/~jdnorton/teaching/GR&Grav_2007/pdf/Einstein_Entwurf_1913.pdf English translate]</ref>

The Einstein field equations are [[Nonlinear differential equation|nonlinear]] and considered difficult to solve. Einstein used approximation methods in working out initial predictions of the theory. But in 1916, the astrophysicist [[Karl Schwarzschild]] found the first non-trivial exact solution to the Einstein field equations, the [[Schwarzschild metric]]. This solution laid the groundwork for the description of the final stages of gravitational collapse, and the objects known today as black holes. In the same year, the first steps towards generalizing Schwarzschild's solution to [[electrical charge|electrically charged]] objects were taken, eventually resulting in the [[Reissner–Nordström metric|Reissner–Nordström solution]], which is now associated with [[charged black hole|electrically charged black holes]].<ref>{{Harvnb|Schwarzschild|1916a}}, {{Harvnb|Schwarzschild|1916b}} and {{Harvnb|Reissner|1916}} (later complemented in {{Harvnb|Nordström|1918}})</ref> In 1917, Einstein applied his theory to the [[universe]] as a whole, initiating the field of relativistic cosmology. In line with contemporary thinking, he assumed a static universe, adding a new parameter to his original field equations—the [[cosmological constant]]—to match that observational presumption.<ref>{{Harvnb|Einstein|1917}}, cf. {{Harvnb|Pais|1982|loc=ch. 15e}}</ref> By 1929, however, the work of [[Edwin Hubble|Hubble]] and others had shown that the universe is expanding. This is readily described by the expanding cosmological solutions found by [[Alexander Friedmann|Friedmann]] in 1922, which do not require a cosmological constant. [[Georges Lemaître|Lemaître]] used these solutions to formulate the earliest version of the [[Big Bang]] models, in which the universe has evolved from an extremely hot and dense earlier state.<ref>Hubble's original article is {{Harvnb|Hubble|1929}}; an accessible overview is given in {{Harvnb|Singh|2004|loc=ch. 2–4}}</ref> Einstein later declared the cosmological constant the biggest blunder of his life.<ref>As reported in {{Harvnb|Gamow|1970}}. Einstein's condemnation would prove to be premature, cf. the section [[#Cosmology|Cosmology]], below</ref>

During that period, general relativity remained something of a curiosity among physical theories. It was clearly superior to [[Newtonian gravity]], being consistent with special relativity and accounting for several effects unexplained by the Newtonian theory. Einstein showed in 1915 how his theory explained the [[Perihelion precession of Mercury|anomalous perihelion advance]] of the planet [[Mercury (planet)|Mercury]] without any arbitrary parameters ("[[wikt:fudge factor|fudge factors]]"),<ref>{{Harvnb|Pais|1982|pp=253–254}}</ref> and in 1919 an expedition led by [[Arthur Eddington|Eddington]] confirmed general relativity's prediction for the deflection of starlight by the Sun during the total [[solar eclipse of 29 May 1919]],<ref>{{Harvnb|Kennefick|2005}}, {{Harvnb|Kennefick|2007}}</ref> instantly making Einstein famous.<ref>{{Harvnb|Pais|1982|loc=ch. 16}}</ref> Yet the theory remained outside the mainstream of [[theoretical physics]] and astrophysics until developments between approximately 1960 and 1975, now known as the [[History of general relativity#Golden age|golden age of general relativity]].<ref>{{Harvnb|Thorne|2003|p=[https://books.google.com/books?id=yLy4b61rfPwC&pg=PA74 74]}}</ref> Physicists began to understand the concept of a black hole, and to identify [[quasar]]s as one of these objects' astrophysical manifestations.<ref>{{Harvnb|Israel|1987|loc=ch. 7.8–7.10}}, {{Harvnb|Thorne|1994|loc=ch. 3–9}}</ref> Ever more precise solar system tests confirmed the theory's predictive power,<ref>Sections [[#Orbital effects and the relativity of direction|Orbital effects and the relativity of direction]], [[#Gravitational time dilation and frequency shift|Gravitational time dilation and frequency shift]] and [[#Light deflection and gravitational time delay|Light deflection and gravitational time delay]], and references therein</ref> and relativistic cosmology also became amenable to direct observational tests.<ref>Section [[#Cosmology|Cosmology]] and references therein; the historical development is in {{Harvnb|Overbye|1999}}</ref>

General relativity has acquired a reputation as a theory of extraordinary beauty.<ref name=":0">{{Harvnb|Landau|Lifshitz|1975|loc=p. 228}} "...the ''general theory of relativity''...was established by Einstein, and represents probably the most beautiful of all existing physical theories."</ref><ref>{{Harvnb|Wald|1984|loc=p. 3}}</ref><ref>{{Harvnb|Rovelli|2015|loc=pp. 1–6}} "General relativity is not just an extraordinarily beautiful physical theory providing the best description of the gravitational interaction we have so far. It is more."</ref> [[Subrahmanyan Chandrasekhar]] has noted that at multiple levels, general relativity exhibits what [[Francis Bacon]] has termed a "strangeness in the proportion" (''i.e''. elements that excite wonderment and surprise). It juxtaposes fundamental concepts (space and time ''versus'' matter and motion) which had previously been considered as entirely independent. Chandrasekhar also noted that Einstein's only guides in his search for an exact theory were the principle of equivalence and his sense that a proper description of gravity should be geometrical at its basis, so that there was an "element of revelation" in the manner in which Einstein arrived at his theory.<ref>{{Harvnb|Chandrasekhar|1984|loc=p. 6}}</ref> Other elements of beauty associated with the general theory of relativity are its simplicity and symmetry, the manner in which it incorporates invariance and unification, and its perfect logical consistency.<ref>{{Harvnb|Engler|2002}}</ref>

In the preface to ''[[Relativity: The Special and the General Theory]]'', Einstein said "The present book is intended, as far as possible, to give an exact insight into the theory of Relativity to those readers who, from a general scientific and philosophical point of view, are interested in the theory, but who are not conversant with the mathematical apparatus of theoretical physics. The work presumes a standard of education corresponding to that of a university matriculation examination, and, despite the shortness of the book, a fair amount of patience and force of will on the part of the reader. The author has spared himself no pains in his endeavour to present the main ideas in the simplest and most intelligible form, and on the whole, in the sequence and connection in which they actually originated."<ref>{{cite book |title=Relativity – The Special and General Theory |author1=Albert Einstein |edition= |publisher=Read Books Ltd |year=2011 |isbn=978-1-4474-9358-7 |page=4 |url=https://books.google.com/books?id=yhN9CgAAQBAJ}} [https://books.google.com/books?id=yhN9CgAAQBAJ&pg=PT4 Extract of page 4]</ref>