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In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild solution) is an exact solution to the Einstein field equations that describes the gravitational field outside a spherical mass, on the assumption that the electric charge of the mass, angular momentum of the mass, and universal cosmological constant are all zero.
Trying to find a complete and precise definition of singularities in the theory of general relativity, the current best theory of gravity, remains a difficult problem. [1] [2] A singularity in general relativity can be defined by the scalar invariant curvature becoming infinite [3] or, better, by a geodesic being incomplete. [4]
Karl Schwarzschild (German: [kaʁl ˈʃvaʁtsʃɪlt] ⓘ; 9 October 1873 – 11 May 1916) was a German physicist and astronomer.. Schwarzschild provided the first exact solution to the Einstein field equations of general relativity, for the limited case of a single spherical non-rotating mass, which he accomplished in 1915, the same year that Einstein first introduced general relativity.
A black hole cosmology (also called Schwarzschild cosmology or black hole cosmological model) is a cosmological model in which the observable universe is the interior of a black hole. Such models were originally proposed by theoretical physicist Raj Kumar Pathria , [ 1 ] and concurrently by mathematician I. J. Good .
Lemaître coordinates are a particular set of coordinates for the Schwarzschild metric—a spherically symmetric solution to the Einstein field equations in vacuum—introduced by Georges Lemaître in 1932. [1] Changing from Schwarzschild to Lemaître coordinates removes the coordinate singularity at the Schwarzschild radius.
The Schwarzschild radius was named after the German astronomer Karl Schwarzschild, who calculated this exact solution for the theory of general relativity in 1916. The Schwarzschild radius is given as r s = 2 G M c 2 , {\displaystyle r_{\text{s}}={\frac {2GM}{c^{2}}},} where G is the gravitational constant , M is the object mass, and c is the ...
The Kerr metric or Kerr geometry describes the geometry of empty spacetime around a rotating uncharged axially symmetric black hole with a quasispherical event horizon.The Kerr metric is an exact solution of the Einstein field equations of general relativity; these equations are highly non-linear, which makes exact solutions very difficult to find.
The singularity at the center of a Schwarzschild black hole is an example of a strong singularity. Space-like singularities are a feature of non-rotating uncharged black holes as described by the Schwarzschild metric , while time-like singularities are those that occur in charged or rotating black hole exact solutions.