6 ms·

> The infalling person has no way of knowing, locally, that they have crossed the horizon Is there such a thing as "the" event horizon? Suppose Alice and Bob a

by cvoss 3y ago

> The infalling person has no way of knowing, locally, that they have crossed the horizon Is there such a thing as "the" event horizon? Suppose Alice and Bob are both free falling into a block hole, but Alice is a little bit further in than Bob. Alice sends a message photon straight back out of the gravity well once per second by her pocket watch. There is a distant observer, Dana. Dana believes the event horizon to lie at a certain radius, and as Alice approaches that radius, she appears to Dana to slow down and to redshift so that Dana does not see Alice cross the horizon. However, there is a particular second, N, on Alice's pocket watch which marks the final messenger photon that can get back out to Dana; all messages > N are trapped. Now, if Bob is right behind Alice, falling into the black hole, isn't it possible that he can observe Alice's (N+1)st photon? That photon need not escape the black hole all the way out to Dana in order for Bob to see it, since he's falling toward it. Therefore, doesn't Bob disagree with Dana about where the event horizon is? Alice hasn't crossed it yet as of N+1 as far as Bob can see. I guess my bigger point/question is, if you decide to fall into a black hole, won't its horizon recede before your eyes as you approach?

DavidSJ 3y ago
I haven't ever decided to fall into a black hole so I'm not speaking from experience, but I think Bob would only see Alice's (N+1)st photon after he himself has crossed the event horizon.
- pdonis 3y ago
  > I think Bob would only see Alice's (N+1)st photon after he himself has crossed the event horizon. Yes, this is correct.
pdonis 3y ago
> Is there such a thing as "the" event horizon? Yes. It's a global feature of the spacetime geometry. It's not observer dependent. > if Bob is right behind Alice, falling into the black hole, isn't it possible that he can observe Alice's (N+1)st photon? If he himself crosses the horizon, yes, he will see Alice's N+1st photon after he has crossed the horizon. But not until then. > doesn't Bob disagree with Dana about where the event horizon is? No. See above. > if you decide to fall into a black hole, won't its horizon recede before your eyes as you approach? There are optical effects due to light rays traveling tangentially, not radially, that (if we imagine the horizon as a light-emitting surface, which it actually isn't) could make this seem to happen, but this would be an optical illusion; you would still fall through the horizon regardless of what appearances your eyes were seeing.
- cvoss 3y ago
  For some time after Alice and Bob have both crossed, they can continue to communicate with one another, showing that they are not separated by a horizon. But since Alice is ahead, won't she and Bob get separated more and more over time? Isn't there a time after which Alice can't even get a message out to Bob? Can that not be characterized as an event horizon separating Alice and Bob, and one which is fundamentally distinct from the one separating Alice and Bob from Dana?
  - pdonis 3y ago
    > For some time after Alice and Bob have both crossed, they can continue to communicate with one another Yes. > showing that they are not separated by a horizon. No. They are separated by a horizon, but only for a short time--short enough that Bob crosses the horizon before seeing any light signals emitted upward by Alice after she has crossed the horizon. > since Alice is ahead, won't she and Bob get separated more and more over time? Yes. > Isn't there a time after which Alice can't even get a message out to Bob? Yes. If you draw a spacetime diagram of the hole with Alice's and Bob's worldlines on it (Kruskal coordinates work well for this), then at some point on Alice's worldline her future light cone will no longer include any portion of Bob's worldline; and once she passes that point, she can no longer send light signals to Bob (because he will hit the singularity before her signals can reach him). One can also make a similar argument for Bob. > Can that not be characterized as an event horizon separating Alice and Bob, and one which is fundamentally distinct from the one separating Alice and Bob from Dana? No.
    - cvoss 3y ago
      > No. This answer is pretty terse and doesn't provide a lot of understanding. Found these helpful articles instead, explaining the difference between an absolute horizon [0], which is what you're talking about, and an apparent horizon [1], which is the idea I've been asking about without knowing the magic word for. [0] https://en.wikipedia.org/wiki/Absolute_horizon https://en.wikipedia.org/wiki/Absolute_horizon [1] https://en.wikipedia.org/wiki/Apparent_horizon https://en.wikipedia.org/wiki/Apparent_horizon

by cvoss 3y ago

DavidSJ 3y ago

I haven't ever decided to fall into a black hole so I'm not speaking from experience, but I think Bob would only see Alice's (N+1)st photon after he himself has crossed the event horizon.

pdonis 3y ago
> I think Bob would only see Alice's (N+1)st photon after he himself has crossed the event horizon. Yes, this is correct.

pdonis 3y ago

> Is there such a thing as "the" event horizon? Yes. It's a global feature of the spacetime geometry. It's not observer dependent. > if Bob is right behind Alice, falling into the black hole, isn't it possible that he can observe Alice's (N+1)st photon? If he himself crosses the horizon, yes, he will see Alice's N+1st photon after he has crossed the horizon. But not until then. > doesn't Bob disagree with Dana about where the event horizon is? No. See above. > if you decide to fall into a black hole, won't its horizon recede before your eyes as you approach? There are optical effects due to light rays traveling tangentially, not radially, that (if we imagine the horizon as a light-emitting surface, which it actually isn't) could make this seem to happen, but this would be an optical illusion; you would still fall through the horizon regardless of what appearances your eyes were seeing.

cvoss 3y ago
For some time after Alice and Bob have both crossed, they can continue to communicate with one another, showing that they are not separated by a horizon. But since Alice is ahead, won't she and Bob get separated more and more over time? Isn't there a time after which Alice can't even get a message out to Bob? Can that not be characterized as an event horizon separating Alice and Bob, and one which is fundamentally distinct from the one separating Alice and Bob from Dana?
- pdonis 3y ago
  > For some time after Alice and Bob have both crossed, they can continue to communicate with one another Yes. > showing that they are not separated by a horizon. No. They are separated by a horizon, but only for a short time--short enough that Bob crosses the horizon before seeing any light signals emitted upward by Alice after she has crossed the horizon. > since Alice is ahead, won't she and Bob get separated more and more over time? Yes. > Isn't there a time after which Alice can't even get a message out to Bob? Yes. If you draw a spacetime diagram of the hole with Alice's and Bob's worldlines on it (Kruskal coordinates work well for this), then at some point on Alice's worldline her future light cone will no longer include any portion of Bob's worldline; and once she passes that point, she can no longer send light signals to Bob (because he will hit the singularity before her signals can reach him). One can also make a similar argument for Bob. > Can that not be characterized as an event horizon separating Alice and Bob, and one which is fundamentally distinct from the one separating Alice and Bob from Dana? No.
  - cvoss 3y ago
    > No. This answer is pretty terse and doesn't provide a lot of understanding. Found these helpful articles instead, explaining the difference between an absolute horizon [0], which is what you're talking about, and an apparent horizon [1], which is the idea I've been asking about without knowing the magic word for. [0] https://en.wikipedia.org/wiki/Absolute_horizon https://en.wikipedia.org/wiki/Absolute_horizon [1] https://en.wikipedia.org/wiki/Apparent_horizon https://en.wikipedia.org/wiki/Apparent_horizon