- #1

PWiz

- 695

- 116

I've checked my maths but I'm still not sure if this formula is correct, because I immediately noticed that the formula appears to violate the second postulate of the special theory of relativity in a particular case. If ##M## is considered to be spherical and have a radius of ##x## where ##x<\frac{2GM}{c^2}##(by substituting v with c) with most of it's mass concentrated at the center, then any object moving towards this mass from infinity will exceed the speed of light when ##r## becomes less than ##\frac{2GM}{c^2}##(i.e. when the object moving towards ##M## enters the region between ##x## and ##\frac{2GM}{c^2}##). This also means that the escape velocity for a distance less than ##\frac{2GM}{c^2}## from ##M## will be unachievable, which doesn't make any sense. Where have I gone wrong?