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A Schwarzschild black hole is described by the Schwarzschild metric, and cannot be distinguished from any other Schwarzschild black hole except by its mass. The Schwarzschild black hole is characterized by a surrounding spherical boundary, called the event horizon , which is situated at the Schwarzschild radius ( r s {\displaystyle r_{\text{s ...
In deriving the Schwarzschild metric, it was assumed that the metric was vacuum, spherically symmetric and static. The static assumption is unneeded, as Birkhoff's theorem states that any spherically symmetric vacuum solution of Einstein's field equations is stationary; the Schwarzschild solution thus follows.
Its chief disadvantage is that in those coordinates the metric depends on both the time and space coordinates. In Eddington–Finkelstein, as in Schwarzschild coordinates, the metric is independent of the "time" (either t in Schwarzschild, or u or v in the various Eddington–Finkelstein coordinates), but none of these cover the complete spacetime.
The Schwarzschild solution supposes an object that is not rotating in space and is not charged. To account for charge, the metric must satisfy the Einstein field equations like before, as well as Maxwell's equations in a curved spacetime. A charged, non-rotating mass is described by the Reissner–Nordström metric.
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 Schwarzschild metric is named in honour of its discoverer Karl Schwarzschild, who found the solution in 1915, only about a month after the publication of Einstein's theory of general relativity. It was the first exact solution of the Einstein field equations other than the trivial flat space solution .
In the Schwarzschild coordinates, the Schwarzschild radius = is the radial coordinate of the event horizon = =. In the Kruskal–Szekeres coordinates the event horizon is given by =. Note that the metric is perfectly well defined and non-singular at the event horizon.
The Schwarzschild metric of a black hole and the Kerr metric of a rotating black hole are common examples of stationary spacetimes. By definition, a stationary spacetime exhibits time translation symmetry. This is technically called a time-like Killing vector. Because the system has a time translation symmetry, Noether's theorem guarantees that ...