Firewall solution for black hole paradox and creation of black event horizon

Question

AMPS paper [1] proved that black hole complementarity explanation of blackhole paradox requires there is a "firewall": high-energy wall which destroys everything entering event horizon.

However, I'm confused how "firewall" explains the following setup:

• lets assume that are two entangled particles Bob and Alice
• black hole event horizon is created in space between these two particles
• Bob is now behind black hole event horizon while Alice is outside
• Now black-hole evaporates and you have again Alice entangled with more than two particles

So how "firewall" solves this?

UPDATE: Here is my thought experiment how to create black hole by horizon appearing - not growing. Lets assume that is absolutely nothing around Bob. Then you can create light rays pointing to Bob from far far away. If you have enough of these light rays, you will create event horizon around Bob before light rays even reach Bob. So Bob will not be swallowed by growing event horizon and event horizon will just appear around Bob.

[1] http://arxiv.org/abs/1207.3123

Answer 1

You can't just create event horizons of finite area out of thin air like that.

Let me explain with a very idealized thought experiment: imagine you have a thin spherically symmetric shell of dust particles of radius $R$ and total mass $M$. Say that initially $R > r_s$ (where $r_s = 2M$ in natural units). Say that the particles are initially at rest so that they will inevitably collapse under their mutual gravitational attraction, that is, the radius of the shell will decrease with time. Eventually the radius will become smaller than $r_s$ and the dust particles will be gobbled up by the event horizon. You are left with something that to the outside observer is indistinguishable from a Schwarzschild black hole.

Now place yourself inside the shell. You calculated that at an instant $t_0$ the dust shell will reach the Schwarzschild radius, so you might want to try to escape before an event horizon forms and you are irrevocably trapped.

Because the shell is spherically symmetric, the metric inside is flat, so you can just use special relativity to figure this out. If you are at the center, because you can't exceed the speed of light, you need to give yourself at least $r_s/c$ time before collapse in order to be able to escape. If you wait too long, welp, that's too bad: you're trapped, just as you would be if you had waited until the dust shell reached its Schwarzschild radius.

This implies that a retroactive event horizon has formed whose radius grows linearly with time until it reaches $r_s$. So Bob has actually been swallowed by a growing event horizon. If you believe in firewalls, you must believe this horizon has a firewall, too.