Schwarzschild Radius
Schwarzschild radius a Simple derivation If the radius of a spherical body is less than Schwarzschild radius it is called a black hole. And for a black hole the escape speed is equal to the speed of light. Schwarzschild radius , r s = 2GM / C 2 Usually the solution is obtained from EFE (Einstein’s Field Equation ) Proof For a planet the escape speed is related to its mass and radius , this is obtained by equating kinetic energy to the gravitational potential energy V escape 2 = 2GM / R So for a black hole C 2 =2GM / R And R= r s Therefore r s = 2GM / C 2