Do these particles actually reach future null infinity, and if not where they end up?

In this paper by analogy with a process $$e^+e^-\to e^+e^-$$ Andrew Strominger proposes that in black hole evaporation there is creation of soft photons and gravitons. This can be argued by infrared finiteness or by conservation of Large Gauge Symmetry and BMS charges.

Now, as far as I know, at least for a massless scalar field, the black hole background behaves as a kind of potential barrier $$V(r_\ast)$$ in terms of the tortoise coordinate:

Here $$r_\ast = -\infty$$ is the horizon and $$r_\ast = \infty$$ is null infinity.

Now from this potential it seems that a soft mode, i.e., one with very low energy, simply cannot escape to future null infinity. In other words it seems to reflect back.

Now, if this is also the same for soft photons and gravitons, what happens to these soft photons and soft gravitons Strominger proposes to be produced in black hole evaporation? Do they escape to future null infinity, and if not, where they end up?

Is this somewhat related to the "holographic plate" which Strominger, Hawking and Perry mention in this paper?

• To the best of my understanding, it is not black hole by itself that produces these soft gravitons but a system (black hole + already radiated (hard) quanta of Hawking radiation) or alternatively multiple hard quanta, so your potential and arguments from it are not applicable – A.V.S. Oct 31 '18 at 4:27
• If I understand correctly, these soft photons and gravitons have energy zero, not $\epsilon>0$. This is why the vacuum is infinitely degenerate; adding a zero-energy particle does not change the energy. Therefore, they live at null infinity, and it is not appropriate to treat them as localized particle states. – Dwagg Oct 31 '18 at 13:52
• @A.V.S. I'm not sure that I understand your point. Indeed Strominger suggests that the soft particles are produced as the hard Hawking quanta propagate to future null infinity. Still the potential AFAIK is not associated to particles produced by the black hole, but it affects any mode of a quantum field propagating in a black hole spacetime. In particular, since these particles would be excitations of a quantum field which do propagate in a black hole spacetime, I think the potential would affect them anyway. – user1620696 Nov 1 '18 at 2:55
• The “soft gravitons” could, of course, feel that potential (or rather its variation appropriate for their species), but they are not obliged to tunnel through it. They are born away from the horizon and become real not as participants of pair creation via tunneling but as part of interaction with long range fields. – A.V.S. Nov 1 '18 at 5:02