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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?
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.
The Schwarzschild solution describes spacetime under the influence of a massive, non-rotating, spherically symmetric object. It is considered by some to be one of the simplest and most useful solutions to the Einstein field equations. [citation needed]
Derivation Of The Schwarzschild Radius Without General Relativity. In this paper I present an alternative method of deriving the Schwarzschild radius of a black hole. The method uses three of the Planck units formulas: the Planck mass, the Planck momentum and the Planck length.
The derivation of this effect, known as Hawking radiation, involves the use of quantum field theory in curved spacetime and is way outside our scope right now. The informal idea is nevertheless understandable.
Equations taken directly from Einstein’s rst paper [3], and these tools will be utilized to derive the Einstein equations and the Schwarzschild solution to the equations and understand their implications on physical phenomena.
The goal of this document is to provide a full, thoroughly detailed derivation of the Schwarzschild solution. Much of the differential geometric foundations can be found elsewhere (and may be added at a later date).
