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At a supermassive black hole's event horizon the escape speed is, of course, the speed of light.

At the same time, Newton's Law of Gravitation $F=G* m1*m2/r^2$ would predict that the gravitational field strength could be very weak if the black hole is massive enough.

Does it mean that you could escape this black hole if you had continuous propulsion?

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  • $\begingroup$ Newton's law of gravitation is not valid at high speeds and at high gravitational fields. So for the analysis of large supermassive black holes (those having enormous gravitational fields) and to study what happens near event horizon (where the speed of the object is nearly the speed of light), you may consider a valid theory- The General Theory of Relativity (which predicted the existence of black holes and the associated concept of event horizon). Newton's theory is a special case of the general theory- a low gravitational field, low speed limit $\endgroup$ – UKH Jan 13 '17 at 15:10
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Newton's law of gravitation predicts that you could escape a black hole without ever exceeding the speed of light (your speed as measured in the Galilean frame where the black hole is stationary), sure. You can do this (in Newtonian physics) by using continuous propulsion.

Newton's laws predict plenty of other wrong things when used outside their realm of validity, too! In general and special relativity going faster than light breaks causality, and inside the event horizon of a black hole, every path which travels slower than the speed of light (including the constantly accelerating ones) hits the singularity. This is a result which requires general relativity to prove. It is outside the realm of Newtonian physics!

In summation: No, once you're past the event horizon, even with any constant acceleration radially outwards, you will still hit the singularity.

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"Force of gravity" means that there is a constant exchange of momentum happening between gravitating objects.

In the case of a supermassive black hole and a rocket near its event horizon the force of gravity is weak, because during one second just a moderate amount of momentum is exchanged between those two things.

That's how it makes sense to say the force of gravity is small.

BUT that second is a non-time dilated second. During one second according to a clock inside the rocket a very large amount of momentum gets exchanged. That's why the rocket has to be ridiculously powerful to ascend.

Of course if we say that the force of gravity of a supermassive black hole is weak, then we should also say that the thrust of a rocket is weak, when said rocket is climbing up from the neighborhood of said black hole without accelerating much.

But the passengers in that rocket say the force of gravity is very large and the force produced by the rocket motors is very large.

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The quick answer here is that when you are inside of the event horizon the space time is so heavily distorted that all possible directions of motion are pointing towards the black hole. In that sense it doesn't matter how much you fire you engine, you will not escape anyway.

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If you are inside the event horizon there is no escape. You are perhaps being confused by discussions of the weakness of tidal forces near supermassive BH. The gravitational field itself is not weak because the mass of the BH offsets any decrease due to the EH radius. Oh BTW the classical Newtonian gravity equations would not apply anyway.

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protected by Qmechanic Jan 12 '17 at 17:56

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