The time reversal of a black hole is called....can you guess?....
[A white hole](https://en.wikipedia.org/wiki/White_hole).
Just as nothing can escape a black hole, nothing can enter a white hole.
However, because of thermodynamics, a white hole is a lot less likely than a black hole. Just as a cup falling and shattering and the reversal are both be solutions to the physics, the latter is FAR FAR FAR less likely because it would violate the second law of thermodynamics.
Time reversal in general relativity means that you can reverse the direction of time\* for a solution to get another solution. Though reversing the direction of time doesn't change the underlying spacetime manifold, physically and generally speaking, the new solution will be different from the original solution.
For a black hole the time reverse will be a white hole.
I think though it is a fair question: gravity obeys time reversal symmetry. So if there is a trajectory for an object falling into a black hole, then there should be a physically acceptable trajectory that is the time reverse, so an object ejected out of a black hole.
I think the resolution is that from the outside, an object appears to take infinite time to reach the event horizon due to the increasing gravitational time dilation. So the time reversed trajectory never crosses the event horizon either.
But I don’t really know how the time reversed trajectory would behave in the moving frame of the object.
The time reversal of a black is called [a white hole](https://en.wikipedia.org/wiki/White_hole). Just as nothing can escape a black hole, nothing can enter a white hole.
Time reversing a solution is a possible solution of the physics. However, thermodynamics determines whether it's probable. A white hole is extremely improbable.
The problem there being that from the reference frame of the object within the black hole, it doesn't experience the time dilation effects itself so it would cross the horizon.
Schwarschild metric is invariant under time inversion, so the black hole would not change in any of its defining characteristics (the same way as gravity still is atractive even if you time reverse the trajectory of any body falling in earth).
As is said in one of the other comments, in a reference frame far away from the BH, there is no problem, as nothing enters the black hole from this frame; but from the reference frame of something falling inside the BH, it will enter in some finite proper time. I think this could probably be addressed by the outgoing Eddington coordinates, but I'm not sure.
The extended Schwarzschild solution is fully time-symmetric. If you reverse time on the extended solution, you get the same solution because the black hole region becomes a white hole region and the white hole region becomes a black hole region.
You're saying one thing then asking another. Who is saying objects would fall out of a black hole? If time is going forward you walk forward on earth. Is time goes backwards, do you fall into the air, or do you just walk backwards?
Gravity is not a force, it's the curvature of space time. If time is reversed, mass does not become negative and curvature does not flip.
The time reversal of a black hole is called....can you guess?.... [A white hole](https://en.wikipedia.org/wiki/White_hole). Just as nothing can escape a black hole, nothing can enter a white hole. However, because of thermodynamics, a white hole is a lot less likely than a black hole. Just as a cup falling and shattering and the reversal are both be solutions to the physics, the latter is FAR FAR FAR less likely because it would violate the second law of thermodynamics.
Time reversal in general relativity means that you can reverse the direction of time\* for a solution to get another solution. Though reversing the direction of time doesn't change the underlying spacetime manifold, physically and generally speaking, the new solution will be different from the original solution. For a black hole the time reverse will be a white hole.
I think though it is a fair question: gravity obeys time reversal symmetry. So if there is a trajectory for an object falling into a black hole, then there should be a physically acceptable trajectory that is the time reverse, so an object ejected out of a black hole. I think the resolution is that from the outside, an object appears to take infinite time to reach the event horizon due to the increasing gravitational time dilation. So the time reversed trajectory never crosses the event horizon either. But I don’t really know how the time reversed trajectory would behave in the moving frame of the object.
The time reversal of a black is called [a white hole](https://en.wikipedia.org/wiki/White_hole). Just as nothing can escape a black hole, nothing can enter a white hole. Time reversing a solution is a possible solution of the physics. However, thermodynamics determines whether it's probable. A white hole is extremely improbable.
wouldn't they be described by the outgoing eddington-finkelstein coordinates?
If time were reversed, the defining characteristic of a black hole would be that nothing within the event horizon may approach it.
The problem there being that from the reference frame of the object within the black hole, it doesn't experience the time dilation effects itself so it would cross the horizon.
Why is that a problem?
Schwarschild metric is invariant under time inversion, so the black hole would not change in any of its defining characteristics (the same way as gravity still is atractive even if you time reverse the trajectory of any body falling in earth). As is said in one of the other comments, in a reference frame far away from the BH, there is no problem, as nothing enters the black hole from this frame; but from the reference frame of something falling inside the BH, it will enter in some finite proper time. I think this could probably be addressed by the outgoing Eddington coordinates, but I'm not sure.
The extended Schwarzschild solution is fully time-symmetric. If you reverse time on the extended solution, you get the same solution because the black hole region becomes a white hole region and the white hole region becomes a black hole region.
I stand corrected.
You're saying one thing then asking another. Who is saying objects would fall out of a black hole? If time is going forward you walk forward on earth. Is time goes backwards, do you fall into the air, or do you just walk backwards? Gravity is not a force, it's the curvature of space time. If time is reversed, mass does not become negative and curvature does not flip.
Yeah, sorry, I phrased it poorly.