The Schwarzschild solution, which makes use of Schwarzschild coordinates and the Schwarzschild metric, leads to a derivation of the Schwarzschild radius, which is the size of the event horizon of a non-rotating black hole.
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In only a few years of work ( by 1916 he had died from a chronic illness ) he had made fundamental contributions in astrophysics and to Schwarzschild solution " and which is of fundamental importance for the theory of black holes.
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For the Schwarzschild solution ( which is the simplest possible spacetime surrounding a massive object ), the same acceleration as that which ( in Newtonian physics ) is created by gravity is obtained when a constant of integration is set equal to " 2MG / c 2 " ).
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The theory shows some promise for the treatment of black holes, as its form of the Schwarzschild solution does not break down at singularities; most of the results of general relativity have been mathematically reproduced, and the relativistic formulation of classical electrodynamics has been extended to quantum mechanics and the Dirac equation.
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The Schwarzschild solution is the simplest spherically symmetric solution of the Einstein equations with zero cosmological constant, and it describes a black hole event horizon in otherwise empty space . de Sitter Schwarzschild is a combination of the two, and describes a black hole horizon spherically centered in an otherwise de Sitter universe.
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For example, the Schwarzschild solution has a Killing algebra of dimension 4 ( 3 spatial rotational vector fields and a time translation ), whereas the Friedmann-Lema�tre-Robertson-Walker ( FLRW ) metric ( excluding the Einstein static subcase ) has a Killing algebra of dimension 6 ( 3 translations and 3 rotations ).
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In other words, the Schwarzschild solution can be applied, provided that the " M " + " m " is used in place of " M " in the formulae for the Schwarzschild radius " r " " s " and the precession angle per revolution ??.
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In the Schwarzschild solution, it is assumed that the larger mass " M " is stationary and it alone determines the gravitational field ( i . e ., the geometry of space-time ) and, hence, the lesser mass " m " follows a geodesic path through that fixed space-time.
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In Einstein's theory of general relativity, the "'Schwarzschild metric "'( also known as the "'Schwarzschild vacuum "'or "'Schwarzschild solution "') is the 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.
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For the Schwarzschild solution, we take k ^ a to be the time translation Killing vector k ^ a \ partial _ a = \ frac { \ partial } { \ partial t }, and more generally for the Kerr-Newman solution we take k ^ a \ partial _ a = \ frac { \ partial } { \ partial t } + \ Omega \ frac { \ partial } { \ partial \ phi }, the linear combination of the time translation and axisymmetry Killing vectors which is null at the horizon, where \ Omega is the angular velocity.
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