57 ms·

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 si

by 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
  - pdonis 3y ago
    > This answer is pretty terse and doesn't provide a lot of understanding. Yes, sorry, I was pressed for time. I'll try to expand on it further below. Unfortunately, "apparent horizon" is not the idea you were asking about. I don't know if there is a standard name for the idea you were asking about, but I do know that none of the "horizon" terms we have been using ("event horizon", "absolute horizon", or "apparent horizon") are it. "Absolute horizon" and "event horizon" mean the same thing: they are the boundary of a black hole. This boundary is a global null surface that bounds a region of spacetime that cannot send light signals to infinity. "Apparent horizon" means a surface at which radially outgoing light rays do not move outward. In other words, if you imagine a 2-sphere emitting light rays radially outward in all directions, normally those light rays, taken all together, will form their own 2-sphere that expands with time (its radius increases). If the 2-sphere emitting those light rays is part of an apparent horizon, however, the 2-sphere formed by the light rays does not expand--it keeps the same radius, which means it stays right at the apparent horizon instead of expanding outward away from it. What you were describing, the boundary that describes when Alice can no longer send messages to Bob, is the future light cone of some event on Alice's worldline--the first event whose future light cone does not include any events on Bob's worldline. If you look at the light rays emitted by Alice that form her future light cone, they are not just radially outgoing light rays; the future light cone consists of all light rays emitted at a given event, in all directions, not just radially outward. AFAIK such a surface is never called a "horizon" of any kind; it's a future light cone, which is a different kind of surface.

by cvoss 3y ago

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
- pdonis 3y ago
  > This answer is pretty terse and doesn't provide a lot of understanding. Yes, sorry, I was pressed for time. I'll try to expand on it further below. Unfortunately, "apparent horizon" is not the idea you were asking about. I don't know if there is a standard name for the idea you were asking about, but I do know that none of the "horizon" terms we have been using ("event horizon", "absolute horizon", or "apparent horizon") are it. "Absolute horizon" and "event horizon" mean the same thing: they are the boundary of a black hole. This boundary is a global null surface that bounds a region of spacetime that cannot send light signals to infinity. "Apparent horizon" means a surface at which radially outgoing light rays do not move outward. In other words, if you imagine a 2-sphere emitting light rays radially outward in all directions, normally those light rays, taken all together, will form their own 2-sphere that expands with time (its radius increases). If the 2-sphere emitting those light rays is part of an apparent horizon, however, the 2-sphere formed by the light rays does not expand--it keeps the same radius, which means it stays right at the apparent horizon instead of expanding outward away from it. What you were describing, the boundary that describes when Alice can no longer send messages to Bob, is the future light cone of some event on Alice's worldline--the first event whose future light cone does not include any events on Bob's worldline. If you look at the light rays emitted by Alice that form her future light cone, they are not just radially outgoing light rays; the future light cone consists of all light rays emitted at a given event, in all directions, not just radially outward. AFAIK such a surface is never called a "horizon" of any kind; it's a future light cone, which is a different kind of surface.