I had a lively discussion with a person about black holes recently, and was making the point about gravitational acceleration in GR being paralleled by speed in SR. One thing that I know people talk about with special relativity, is that if you could reach a speed faster than the speed of light then time would reverse (I don't get this as the Lorentz factor gives an imaginary number, and who knows what that means). This is impractical for things with mass due to mass increasing asymptotically with velocity. However, since the event horizon for black hole behaves exactly like asymptotic barrier to reaching the speed of light (we'll say for a stationary non-charged black hole to keep things simple), shouldn't the effects translate to a black hole? Ie once you're in a black hole (ie the mass that was there when the black hole formed), wouldn't the mass be essentially traveling backwards in time, fastest the further it was from the event horizon?
For clarity sake, for matter, approaching the speed of light and approaching the event horizon of black hole are essentially the same with respect to redshift/blueshift, space and time dilation. There for approaching an event horizon from the inside of a black hole would be like de-accelerating toward the speed of light ($v>c$). So matter in a black hole should be falling outward toward the event horizon.
All of this I am of course imagining from the reference frame of a distant observer.
Just curious if I'm way off base on this.
Best Answer
The event horizon of a black hole is a very weird and complicated place. According to my undergrad GR course, at the event horizon of a black hole, time becomes a space-like coordinates, and space becomes a time-like coordinate. From what I remember, a time-like coordinate is one in which you absolutely have to move forward.
Therefore, beyond the black hole horizon, it is impossible to move backwards in space (away from the black hole) in the same manner as it is impossible to move back in time outside of the horizon.
Does it also mean that it is possible to move through time in both direction (time being a space-like coordinate inside the horizon)? Probably, but then, it's still impossible to get out of the black hole, so no one outside would know!
As a side note, according to the holographic principle, information on all events occuring beyond an event horizon is encoded into the event horizon itself, such that it is irrelevant to try to understand what goes on beyond the event horizon. In fact, the very physical existence of something beyond an event horizon is questionable, since it cannot affect us any much more than the event horizon itself can.