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v. t. e. In the general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter within it. [1] The equations were published by Albert Einstein in 1915 in the form of a tensor equation [2] which related the local spacetime curvature (expressed by ...
Solutions of the Einstein field equations are metrics of spacetimes that result from solving the Einstein field equations (EFE) of general relativity. Solving the field equations gives a Lorentz manifold. Solutions are broadly classed as exact or non-exact. The Einstein field equations are.
e. General relativity is a theory of gravitation developed by Albert Einstein between 1907 and 1915. The theory of general relativity says that the observed gravitational effect between masses results from their warping of spacetime. By the beginning of the 20th century, Newton's law of universal gravitation had been accepted for more than two ...
t. e. The Einstein–Hilbert action in general relativity is the action that yields the Einstein field equations through the stationary-action principle. With the (− + + +) metric signature, the gravitational part of the action is given as [1] where is the determinant of the metric tensor matrix, is the Ricci scalar, and is the Einstein ...
The cosmological constant was originally introduced in Einstein's 1917 paper entitled “The cosmological considerations in the General Theory of Reality”. [2] Einstein included the cosmological constant as a term in his field equations for general relativity because he was dissatisfied that otherwise his equations did not allow for a static universe: gravity would cause a universe that was ...
Derivation of the Schwarzschild solution. The Schwarzschild solution describes spacetime under the influence of a massive, non-rotating, spherically symmetric object. It is considered by some to be one of the simplest and most useful solutions to the Einstein field equations . [citation needed]
Albert Einstein. Relativity: the Special and the General Theory, 10th edition (there are a total of 17 editions). ISBN 0-517-029618 at Project Gutenberg; Relativity: The Special and General Theory public domain audiobook at LibriVox; Albert Einstein, Relativity: The Special and General Theory (1920/2000) ISBN 1-58734-092-5 at Bartleby.com
e. In general relativity, an exact solution is a solution of the Einstein field equations whose derivation does not invoke simplifying assumptions, though the starting point for that derivation may be an idealized case like a perfectly spherical shape of matter. Mathematically, finding an exact solution means finding a Lorentzian manifold ...