Hawking radiation: pair production?

[haushofer]

Dear all,

I'm trying to understand the firewall controversy and the role of Hawking radiation in this. To make things concrete, I'll use the desciption of the firewall controversy of John Preskill here,

https://quantumfrontiers.com/2012/12/03/is-alice-burning-the-black-hole-firewall-controversy/

Here he states

Following AMPS, imagine a black hole which is maximally entangled with another quantum system C outside the black hole. Like any black hole, this one evaporates by emitting Hawking radiation. Also following AMPS, assume that the evaporation is unitary, i.e., conserves quantum information. There is strong evidence that unitarity is an inviolable principle of physics, and we don’t really know how to make sense of quantum mechanics without it. Unitarity implies that as a system B is emitted by the black hole in the form of Hawking radiation, this system B, like the black hole from which it emerged, must be maximally entanged with C. And monogamy of entanglement means that B cannot be entangled with anything else besides C.

But this spells trouble for Alice, the brave soul who dares to fall into the black hole. If Alice’s passage through the event horizon were uneventful then she would fall though space that is nearly devoid of particles. But if we cut the empty space seen by Alice into the inside and outside of the black hole at the event horizon, then the particles in system B seen by an observer who stays outside are paired with particles on the inside — B is entangled with a system A inside the horizon, violating the monogamy of entanglement. Something’s wrong.

My question is about the bolded line. Where are those "particles inside the horizon" coming from? Is Hawking-radiation necessarily pair-production of two real entangled particles, of which one goes inside and the other one escapes?

 

[Demystifier]

Is Hawking-radiation necessarily pair-production of two real entangled particles, of which one goes inside and the other one escapes?

Yes.

 

[haushofer]

Ok, I guess that conservation laws dictate pair production then.So what in the mechanism prevents both particles to radiate to infinity or be trapped by the horizon?

 

[Demystifier]

Ok, I guess that conservation laws dictate pair production then.So what in the mechanism prevents both particles to radiate to infinity or be trapped by the horizon?

If they are both trapped or both radiated to infinity, then they cancel each other out so in this case nothing really happens. This is actually the most probable "event", but we only pay attention to the rare events in which something does happen.

Of course, the above is only an intuitive picture (not unlike a picture provided by Feynman diagrams and virtual particles) which should not be taken too seriously.

 

[haushofer]

So what happens in the picture where the actual calculation is performed?

 

[Demystifier]

So what happens in the picture where the actual calculation is performed?

In the actual calculation there is no clear picture of "what really happens". You just calculate the probability density matrix far from the hole.

 

[Haelfix]

The original paper 'particle creation by black holes' is wonderfully readable and clear (its freely available if you google it) and imo more readable than many textbooks on the subject. That traces back the origin of the particles to outgoing and ingoing modes on some spacelike slice.

For the purposes of the firewall argument, what matters more isn't so much questions about the nature of the actual particles perse, but rather the pattern of entanglement. The fact that space inside and outside is split like in a bipartite quantum system and that a very special form of entanglement is necessary for having a vacuum state (Minkowski space).

For a very clear presentation of this decomposition, see
https://arxiv.org/abs/1409.1231

But yes, as far as the original question goes. Having two particles escape to infinity or having them both fall in, can happen, but its not interesting or relevant for the Hawking effect.

 

[haushofer]

Due to social obligations I wasn't able to respond this weekend, but thanks for the answers everyone! I'll take a look at those Jerusalem lectures, and if I have any more question, I'll be back ;)