When does Hawking radiation start?

[regev]

As I understand it, a black hole is supposed to evaporate through Hawking radiation after a long but finite amount of time. Also, the radiation encodes in some sense the information of the matter that fell into the black hole. This according to an observer ("Alice") outside the event horizon.

But according to Alice, when matter ("Bob") does fall into a black hole, time slows down for him so that the amount of time that it takes for him to actually cross the event horizon tends to infinity. (Or is it infinity?)

So how does the Hawking radiation encode Bob's information? Whenever it starts, it can't encode information about matter that hasn't yet crossed the event horizon - that would be info duplication, wouldn't it? So when does information about Bob start to reappear? Billions of years after what?

 

[Demystifier]

The radiation starts even before the horizon forms, so there are no problems with infinite times.

 

[regev]

I disagree. The radiation cannot start before the horizon forms, that is, before the black hole forms. By definition, it is something that happens near the horizon of an existing black hole. I would be interested to hear in what sense can Hawking radiation start before the event horizon is formed.

But my main question is not about that. It is about matter and information that falls into an existing black hole. Let me rephrase: since Relativity says that the fall into the black hole lasts forever, when is the information lost to an observer on the outside and when does it start to reappear as Hawking radiation?

 

[Mentz114]

The event which gives rise to HR happens outside the horizon, and separated from it by a finite distance. If a virtual pair arises, and the anti-particle crosses the horizon, if the remaining particle has sufficient momentum in the outward direction, it can 'escape to infinity'. When this happens is observer dependent.

I think Demystifier used the word 'before' in the spatial, rather than the temporal sense.

 

[Demystifier]

I disagree. The radiation cannot start before the horizon forms, that is, before the black hole forms. By definition, it is something that happens near the horizon of an existing black hole. I would be interested to hear in what sense can Hawking radiation start before the event horizon is formed.

To be precise, I am talking about Hawking radiation from a black hole made by collapsing matter, not from an eternal black hole.
Now, we know that particle creation takes place whenever metric is time dependent. The collapsing matter is just a special case. Therefore, there must be some radiation even before the horizon forms. Of course, without a horizon the distribution of particle energies will not be thermal. Nevertheless, as the metric seen by an external observer gradually approaches the metric of a spacetime with a horizon, the distribution of particles gradually approaches the thermal distribution. As you need an infinite time to create the horizon exactly, the distribution will never be exactly thermal. Nevertheless, in a relatively short time the distribution will be approximately thermal for all practical purposes.

 

[jnorman]

perhaps someone could kindly clear up for me just why only the negative energy part of the virtual pair falls into the BH and the positive energy particle escapes? why can't either fall in with similar frequency? danke.

 

[LURCH]

As I understand it, the Virtual Particle Pair exist in a somewhat "undetermined" state. Which is matter and which is antimatter cannot be determined so long as the pair remain Virtual. When one escapes to reality, its conidition becomes determinate as matter, making the other particle antimatter.

Demystifyer; although I agree with you that "there must be some radiation even before the event horizon forms," I don't think it could be called Hawking Radiation, which is, by definition, formed when one particle falls through an event horizon while the other escapes. Of course, this raises another another question along te same lines as the OP; "How can one particle of a VPP be lost to an outside observer, if it can never fall beyond the EV, from that observers frame?"

 

[Demystifier]

Demystifyer; although I agree with you that "there must be some radiation even before the event horizon forms," I don't think it could be called Hawking Radiation,

But if the horizon is ALMOST formed, would you call this radiation ALMOST Hawking? At least, the distribution will be ALMOST thermal.

 

[Demystifier]

Of course, this raises another another question along te same lines as the OP; "How can one particle of a VPP be lost to an outside observer, if it can never fall beyond the EV, from that observers frame?"

How about ALMOST lost? Indeed, in order to detect this particle, the observer must come VERY close to a surface that represents an "almost" horizon.

 

[Demystifier]

why can't either fall in with similar frequency?

It can. In fact, in most cases this is probably what will happen. However, in such cases these two particles will cancel each other, so no visible phenomenon will remain.