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The Schwarzschild radius or the gravitational radius is a physical parameter in the Schwarzschild solution to Einstein's field equations that corresponds to the radius defining the event horizon of a Schwarzschild black hole. It is a characteristic radius associated with any quantity of mass.
24 cze 2015 · I know that the Schwarzschild radius is given by $$r=\frac{2GM}{c^{2}}.$$ but I never seen a derivation for this equation. 1- Does anyone know how to derive this equation from general relativity?
Schwarzschild radius, the radius below which the gravitational attraction between the particles of a body must cause it to undergo irreversible gravitational collapse. This phenomenon is thought to be the final fate of the more massive stars (see black hole).
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
17 kwi 2024 · The Schwarzschild Radius is a fundamental concept in the study of black holes. It defines the size of the event horizon, the boundary beyond which nothing can escape the gravitational pull of a black hole.
26 kwi 2024 · The Schwarzschild radius is a fundamental property of black holes and is directly related to their formation and behavior. It serves as a measure of the size of a black hole and determines the boundary beyond which nothing can escape its gravitational pull.
To summarize, we have found that the metric of a vacuum spherically symmetric spacetime must take the Schwarzschild form (up to coordinate rede nitions of ocurse). This need not be the case inside of sources, of course.
