- #1
Jim Graham
- 9
- 0
I've been reading about relativity for several years, but I'm no physicist or mathematician. This question has been bothering me lately, and I'm hoping someone out there can help me understand. I don't have the math to express this briefly, so here it is in words...
When a particle of matter crosses the event horizon of a black hole, what is its velocity with respect to the outside? Intuitively, I think that the velocity approaches the speed of light, c, as the particle approaches the horizon. At the point that it would hypothetically cross the horizon, I think that the particle would have the velocity c.
In my mental image of what is happening, I see the particle accelerating as it approaches the horizon. Time dilation makes the particle age more and more slowly relative to the rest of the universe, approaching zero as the particle approaches the horizon.
So, in the proper time of the particle, when it crosses the horizon, what time is it outside of the black hole? I think that the answer must be that an infinite time has passed there. The end of time has come and gone. The universe has ended. There is no universe any more.
If that is true, then why would we expect anything to be "inside" a black hole? There has not been enough time since the beginning of the universe for anything to have crossed an event horizon. From the perspective of the outside universe, the inside of a black hole does not exist, and will never exist as long as the universe outside still exists.
I understand that the inside exists for the particle, and that you can follow the particle across the horizon, using the appropriate coordinate system, and that nothing special happens at the horizon. From the particle’s perspective, the space-time inside the black hole (up to the singularity) seems to be a smooth continuation of the space-time outside of the black hole. That does not mean that it exists during the lifetime of the outside universe.
From this point of view, the “contents” of the black hole are essentially a two-dimensional boundary that surrounds a hole in the universe. The black hole, its event horizon and its central singularity don’t exist. The universe ends at the point just outside of the horizon, which is reached by the in-falling particle only after an infinite (outside) time.
For this to be true, the space near the horizon must be fantastically curved. There has to be enough space there for a particle to travel “forever” at almost the speed of light. How can that be reconciled with the low tidal forces that I’ve heard are found at the event horizons of large black holes? I guess that the answer is that the space is not “curved”, but “radially distorted”. Length contraction of the in-falling particle (from the outside view) does not fully explain this. The in-falling particle would still cover the short distance at the speed of light. It must be that space itself is radially stretched at the event horizon, to allow an infinite time for the particle to reach the horizon.
So is there anything inside a black hole? If so, where have I gone wrong? If not, why do we talk about black holes as if they were objects with an inside? I wonder if there is any essential difference between the end of the universe at the event horizon, and the “plain old” end of the universe everywhere else.
Wondering...Jim
When a particle of matter crosses the event horizon of a black hole, what is its velocity with respect to the outside? Intuitively, I think that the velocity approaches the speed of light, c, as the particle approaches the horizon. At the point that it would hypothetically cross the horizon, I think that the particle would have the velocity c.
In my mental image of what is happening, I see the particle accelerating as it approaches the horizon. Time dilation makes the particle age more and more slowly relative to the rest of the universe, approaching zero as the particle approaches the horizon.
So, in the proper time of the particle, when it crosses the horizon, what time is it outside of the black hole? I think that the answer must be that an infinite time has passed there. The end of time has come and gone. The universe has ended. There is no universe any more.
If that is true, then why would we expect anything to be "inside" a black hole? There has not been enough time since the beginning of the universe for anything to have crossed an event horizon. From the perspective of the outside universe, the inside of a black hole does not exist, and will never exist as long as the universe outside still exists.
I understand that the inside exists for the particle, and that you can follow the particle across the horizon, using the appropriate coordinate system, and that nothing special happens at the horizon. From the particle’s perspective, the space-time inside the black hole (up to the singularity) seems to be a smooth continuation of the space-time outside of the black hole. That does not mean that it exists during the lifetime of the outside universe.
From this point of view, the “contents” of the black hole are essentially a two-dimensional boundary that surrounds a hole in the universe. The black hole, its event horizon and its central singularity don’t exist. The universe ends at the point just outside of the horizon, which is reached by the in-falling particle only after an infinite (outside) time.
For this to be true, the space near the horizon must be fantastically curved. There has to be enough space there for a particle to travel “forever” at almost the speed of light. How can that be reconciled with the low tidal forces that I’ve heard are found at the event horizons of large black holes? I guess that the answer is that the space is not “curved”, but “radially distorted”. Length contraction of the in-falling particle (from the outside view) does not fully explain this. The in-falling particle would still cover the short distance at the speed of light. It must be that space itself is radially stretched at the event horizon, to allow an infinite time for the particle to reach the horizon.
So is there anything inside a black hole? If so, where have I gone wrong? If not, why do we talk about black holes as if they were objects with an inside? I wonder if there is any essential difference between the end of the universe at the event horizon, and the “plain old” end of the universe everywhere else.
Wondering...Jim