2 particles created around event horizon: out or inside?

[nomadreid]

The question is simple, and I have checked the "similar discussions" and googled, but I still come out with various replies. I also know that experimental evidence that could back up the selected choice would be tricky, not to say impossible. But at least according to theory: the entangled particles that would be formed around the event horizon: would they be formed
[1] just outside the event horizon, and one particle falls into the black hole
[2] just inside the event horizon, and one particle tunnels out of the black hole, or
[3] on the event horizon, with one particle appearing inside and one appearing outside, or
[4] the question is meaningless.

 

[Grinkle]

I don't recall the particles being described as entangled, but I have no idea if they would be or not.

To my lay understanding, uncertainty allows for either 1,2 or 3 to occur but if its 1 or 3, I don't think the net change of particles inside the event horizon is negative.

 

[Grinkle]

Hmmm. Is it really correct that case 1 can happen? If so, it seems to me that the black hole gains one particle. If that is so in case 1, is there theory to predict that case 2 happens more often than case 1 so that one would expect evaporation as opposed to stability or growth?

I am not sure if case 3 is different after the outcome than either case 1 or or case 2, I guess I mean case 3 might not really exist in anything but a mathematical sense.

 

[mathman]

One description I have seen is that the event horizon is not sharp. The two particles form in the fuzzy region with one going in and the other going out.

 

[nomadreid]

I don't recall the particles being described as entangled, but I have no idea if they would be or not.

Yes, they are definitely entangled. This is what gave rise to this whole flurry around the firewall paradox. (Although I don't completely understand this. I haven't figured out why, without the firewall, the particle inside would necessarily be entangled not only with the outgoing particle but also all the particles which had been "emitted" from the black hole earlier (which then leads to a contradiction). If anyone can explain that point to me, I would be grateful.

Hmmm. Is it really correct that case 1 can happen? If so, it seems to me that the black hole gains one particle. If that is so in case 1, is there theory to predict that case 2 happens more often than case 1 so that one would expect evaporation as opposed to stability or growth?

The explanation given by those favoring [1] is connected with the energy of the infalling particle: that with respect to an outside observer, the outgoing particle would have positive energy, so that the infalling particle would necessarily have negative energy (or, if you object to the phrase "negative energy" here, say that if the outgoing particle adds energy to the equation situation, the infalling one must subtract it), and it is this subtraction of energy that would be greater than the energy added to the black hole by the infalling (anti)particle. Thus, a sum evaporation.

 

[nomadreid]

One description I have seen is that the event horizon is not sharp. The two particles form in the fuzzy region with one going in and the other going out.

In other words, [4].