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?
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$\begingroup$ It's all about space and time and what is the direction forward in time. A roughly equivalent question would be "can a body travel backwards in time by being thrusted?" $\endgroup$– Andrew SteaneCommented Sep 27, 2023 at 12:03
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$\begingroup$ Not directly related to your question, but you said, "Rockets can escape Earth with lower than escape velocity if constantly thrusted." That depends on what you think "escape" means. Some might say that the rocket has not "escaped" from Earth unless you can turn off the motor and it doesn't fall back. But if it doesn't fall back when you turn off the motor, then that means that it is moving faster than escape velocity. [Note: escape velocity is not a single number. It's a function of distance from the center of the gravitating body. The further out you get, the lower the escape velocity.] $\endgroup$– Solomon SlowCommented Sep 27, 2023 at 14:46
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2 Answers
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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.
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$\begingroup$ Thanks , But didn't understand the equation as I have just finished Highschool physics. But I did understand that the answer is No $\endgroup$– ZeesanCommented Sep 27, 2023 at 7:53
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$\begingroup$ Maybe, I have been too technical. The point is that the special fact about time is that it must preserve causality, this means that there is a privileged direction of time flowing: from past to future. Whereas for spatial coordinates there isn't this type of constraint, you can go from right to left and vice versa. Inside a black hole, space behaves like time and time like space, implying that an observer does not have any other option than falling forward: from the event horizon to the singularity, as well as out of a black hole an observer does not have the option of going backward in time. $\endgroup$– T. ssPCommented Sep 27, 2023 at 11:32
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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.
