Can a body escape a black hole by being thrusted?

Question

I am told many time that nothing can escape black-hole because black-holes escape velocity is more than speed of light. But we know object don't necessarily have to exceed speed of light to escape a gravitational body. Rockets can escape earth with lower than escape velocity if constantly thrusted. In the same way would it be possible to make an object cross event horizon from inside by constantly pushing?

Answer 1

The quick answer is no because time and spatial coordinates twist roles. As well as you can only move in one direction in time (forwards), inside a black hole you can't go backward in the radial coordinate. Looking at the invariant arc length of a static and spherical black hole, neglecting angular motions (Schwarzschild-type): $$ds^2 = -\left(1 - \frac{r_s}{r} \right)dt^2 + \frac{dr^2}{1 - \frac{r_s}{r}},$$ where $r_s$ is the event horizon radius, we see that for $r<r_s$ the temporal coordinate pass to be positive whereas the radial coordinate pass to be negative: $$ds^2 = \left|\left(1 - \frac{r_s}{r} \right) \right|dt^2 - \frac{dr^2}{\left|1 - \frac{r_s}{r}\right|}, r<r_s.$$

Time behaves like space, and space behaves like time inside a black hole.

T.

Answer 2

A less technical answer: a black hole is defined as an object that has a horizon from which nothing can escape from the inside to the outside. This also holds for light, which is the fastest anything can move. So the answer to your question is: no, nothing can escape.

So a black hole is an object very different from any other massive object in our universe.

It is all well and good to define a blak hole in such a way, but the question then is: do black holes really exist? The answer to that question is a clear yes. General Relativity predicts their existence, and maybe even more fascinating, black holes have been observed by astronomers.

If you want to understand technically why that is the case, the best thing you can do is study physics at university. Mind you, General Relativity is not something they will teach you in the first few years.

Disclaimer: a black hole is a concept from classical physics and my answer is valid in that framework. If you consider quantum physics then there is something called Hawking radiation, which says that light can, in fact, escape a black hole, albeit in such a small amount that it can probably never be observed (and that is even further down the physics curriculum). It is also fair to say that a fully fledged consistent theory of general relativity and quantum physics is lacking so you may still be able to contribute to a complete understanding of black holes as a future physicist.