The radius of the event horizon of a black hole (the point at which it is impossible to escape the black hole because the escape velocity would exceed the speed of light) is given by the formula r = 2Gm/c^2, where G is the gravitational constant, c is the speed of light, and m is the mass of the black hole.

Question

Rearrange this formula to isolate c.

Answer 1

r = 2Gm/c^2
c^2 = 2Gm/r
now just take the square root.

Answer 2

r= 2Gm/c^2

rc^2=2Gm

c^2=(2Gm)/r

c=+or- sqrt[(2Gm)/r]

c= sqrt[(2Gm)/r] (the speed of light is positive)