Question

Explain the formula :
$v = \sqrt{2 gm \div r} \leqslant c$
where v is the escape velocity,
g is universal gravitational constant,
m is mass of the body ,
r is radius of black hole &
c is speed of light .

Answer 1

In General relativity, energy formula of a body thrown straight up to the infinity is

E=mc21−RS/R−−−−−−−√

As we know relativistic energy formula is

E=mc21−v2/c2−−−−−−−√

So

mc21−v2e/c2−−−−−−−√=mc21−RS/R−−−−−−−√

hence escape velocity equation in General relativity is

v2e=c2RSR

where RS=2GM/c2 - Schwarzschild radius of a black hole, and R>RS

It's easy to derive that

ve=cRSR−−−√=2GMR−−−−√

So escape velocity formula in General relativity and Newton gravity is the same.

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