When does Hawking radiation begin?

[PAllen]

This question has bothered me sometimes. For 'standard' black hole with an event horizon, an external observer never sees matter cross the horizon (or get any signal from inside); while an infalling observer crosses the horizon and, for a very big black hole, may not even notice any extreme stresses until well inside the horizon. The outside observer does see the the horizon region (if there is no more infalling matter) become very black in finite time as less and less light escapes.

Ok, so assuming we have a black hole form in an isolated region, from an actual collapse, at what point does hawking radiation start being emitted?

It almost seems that we must answer: when, to an ouside observer, did infalling matter really cross the horizon, even though such observer can't see it? This seems like a dubious question. Perhaps the quantum viewpoint gives it a real answer, maybe even a tautological answer: when hawking radiation started (!?)

(For this question, please ignore questions like cosmic background radiation being hotter than the black hole; let's pretend no big bang, and that the only things in the universe are the collapsing matter and one observer far enough away to have a stable orbit).

 

[bcrowell]

Ok, so assuming we have a black hole form in an isolated region, from an actual collapse, at what point does hawking radiation start being emitted?

This isn't really an answer to your question, but it isn't just the event horizon of a black hole that emits Hawking radiation. E.g., an accelerating observer in Minkowski space sees a horizon, and that horizon emits Hawking radiation -- as seen by that observer.

 

[PAllen]

This isn't really an answer to your question, but it isn't just the event horizon of a black hole that emits Hawking radiation. E.g., an accelerating observer in Minkowski space sees a horizon, and that horizon emits Hawking radiation -- as seen by that observer.

I've seen sources that say:

1) the radiation seen by an accelerated observer is Unruh radiation
2) 'everyone' accepts the Unruh effect, but not everyone accepts Unruh radation
3) it is hypothesized that Unruh radiation may have something to do with the Rindler horizon, but not at all established.

Maybe these are old sources?

 

[PAllen]

I've seen sources that say:

1) the radiation seen by an accelerated observer is Unruh radiation
2) 'everyone' accepts the Unruh effect, but not everyone accepts Unruh radation
3) it is hypothesized that Unruh radiation may have something to do with the Rindler horizon, but not at all established.

Maybe these are old sources?

Be that as it may, I have wondered (knowing about Unruh radiation and also radiation of uniformly accelerated charges) whether maybe matter in a sufficiently strong gravitational field radiates. I considered this sort of a weird, speculative, thought.

 

[yuiop]

It would seem reasonable to assume that Hawking radiation starts to radiate from a black hole as soon as the mass compresses to a volume smaller than the Schwarzschild radius and an event horizon forms. Now in theory, if the radiation was emitted exactly from the event horizon, then it would take an infinite amount of time to reach to be detected by a distant observer and the radiation would be redshifted to such a huge extent that it would be almost impossible to detect. For these reasons (and others) I think the radiation is considered to be emitted from just outside the event horizon and in that case the radiation would be detected in a finite time. Just exactly how long would depend on exactly how far outside the event horizon is considered to be "just outside" and that probably requires quantum mechanics to answer. On the other hand Unrah radiation in flat space is just a function of the state of acceleration of the observer and maybe the Hawking radiation from a black hole is just Unrah radiation and in that case the stationary observer in a gravitational field would observe radiation long before the black hole actually formed which would imply that Hawking radiation does not require an actual event horizon to be present. Hmmmm... just musing...

 

[rolandpj]

"as soon as the mass compresses to a volume smaller than the Schwarzschild radius and an event horizon forms"

I think that's a standard misunderstanding. For an external observer (in this case the recipient of Hawking radiation), an event horizon never forms. Or stated equivalently, the formation of an event horizon takes an infinite time for an external observer that does not cross the event horizon.

So, unless there are event horizons that have existed forever (since the big bang, for example), then Hawking radiation (in your twin-particle view) begins now. In other words, for any future black hole that forms (for some observer), there will be spontaneous particle pairs, one of which is destined to be consumed by the black hole, and one of which escapes.

However, the theoretical derivation of Hawking radiation has nothing to do with local effects like particle pairs. The latter is merely a nice way to think about what might be happening. General relativity has nothing to say about quantum effects. And the theoretical derivation of Hawking radiation makes substantial assumptions about the interaction of quantum fields and GR.

And I don't really understand any of this.

Roland

 

[PAllen]

This thread has been answered here:

https://www.physicsforums.com/showthread.php?t=449457