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, rs = 2GM / C2   
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

Vescape 2  = 2GM / R

So for a black hole  C2 =2GM / R
And R= rs
Therefore
rs = 2GM / C2    


Comments

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