Beta Phase: Square45 is currently in beta testing. Expect some features or content to be incomplete or missing.
45

Schwarzschild Radius

The radius of the event horizon of a non-rotating black hole, calculated as R=2GM/c2R = 2GM/c^2, where G is the gravitational constant and c is the speed of light.
📜

The statement of the theorem

For a static, spherically symmetric spacetime described by the Schwarzschild metric ds2=(12GMrc2)c2dt2+(12GMrc2)1dr2+r2dΩ2ds^2 = -\left(1 - \frac{2GM}{r c^2}\right) c^2 dt^2 + \left(1 - \frac{2GM}{r c^2}\right)^{-1} dr^2 + r^2 d\Omega^2, the Schwarzschild radius RsR_s is defined by the location where the coefficient of dt2dt^2 vanishes, yielding: Rs=2GMc2R_s = \frac{2GM}{c^2}
Source: Wikipedia