Escape Velocity and Black Holes

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It is my understanding of black holes that nothing can escape them because their escape velocity is higher than the speed of light. The place at which the escape velocity becomes higher than the speed of light is known as the event horizon. My question is what happens if there is a normal force in the black hole that combats the gravitational potential force? Could something not escape then?
 

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phinds
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It is my understanding of black holes that nothing can escape them because their escape velocity is higher than the speed of light. The place at which the escape velocity becomes higher than the speed of light is known as the event horizon.
Right.

My question is what happens if there is a normal force in the black hole that combats the gravitational potential force? Could something not escape then?
Huh? I have no idea what you mean but nothing can escape from inside the EH of a BH.
 
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Ibix
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Gravity in general relativity is not a force; it is a curvature of spacetime. The event horizon is the surface at which the curvature becomes strong enough that all possible paths lead inwards to the singularity. There are no paths out of the black hole, even under power. This is different from the Newtonian conception of a black hole, from which you could escape with a sufficiently powerful rocket as you suggest.
 
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PeterDonis
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It is my understanding of black holes that nothing can escape them because their escape velocity is higher than the speed of light.
This is a common way of putting it, but it is only heuristic. Strictly speaking, the concept of "escape velocity" doesn't make sense at or inside the horizon of a black hole. A more precise way of defining a black hole is that it is a region of spacetime that cannot send light signals out to infinity. See further comments below.

My question is what happens if there is a normal force in the black hole that combats the gravitational potential force?
In GR, gravity is not a force, and the reason light can't escape from a black hole is not that there is a force pulling it in. The reason is that spacetime is curved in such a way that there aren't any light paths that go from the black hole region out to infinity. This will be true regardless of what other forces are present.

For an example of a black hole with a non-gravitational force present, check out the Reissner-Nordstrom geometry:

https://en.wikipedia.org/wiki/Reissner–Nordström_metric

This is a charged black hole with a static electric field. It still has an event horizon, and it's still impossible for anything to escape from inside the horizon, even though the force due to the electric field repels positive charges.
 

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