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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 Einstein's theory of general relativity, the interior Schwarzschild metric (also interior Schwarzschild solution or Schwarzschild fluid solution) is an exact solution for the gravitational field in the interior of a non-rotating spherical body which consists of an incompressible fluid (implying that density is constant throughout the body) and has zero pressure at the surface.
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.
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.
Gullstrand–Painlevé coordinates are a particular set of coordinates for the Schwarzschild metric – a solution to the Einstein field equations which describes a black hole. The ingoing coordinates are such that the time coordinate follows the proper time of a free-falling observer who starts from far away at zero velocity, and the spatial ...
In general relativity, the Oppenheimer–Snyder model is a solution to the Einstein field equations based on the Schwarzschild metric describing the collapse of an object of extreme mass into a black hole. [1] It is named after physicists J. Robert Oppenheimer and Hartland Snyder, who published it in 1939. [2]
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.
In the mathematical description of general relativity, the Boyer–Lindquist coordinates [1] are a generalization of the coordinates used for the metric of a Schwarzschild black hole that can be used to express the metric of a Kerr black hole. The Hamiltonian for particle motion in Kerr spacetime is separable in Boyer–Lindquist coordinates.