In 2016 Strominger, Hawking and Perry published the paper "Soft Hair on Black Holes" proposing new results that could have importance to the study of the black hole information problem.
One particular result they mention in section 5, that whenever charged matter crosses the horizon, soft photons on the horizon are excited. I believe the same is true for soft gravitons when any matter crosses the horizon.
On the other hand, a series of three papers tackled the problem in more generality from a distinct line of thought. These papers are:
The topic of the three papers is the IR sector and what it has to say about correlations. In the first paper they deal with the usual Bloch-Nordsieck approach of considering inclusive cross sections to avoid IR divergences. In the second paper they talk about the Faddev-Kulish method of dressing asymptotic states with clouds of soft photons or gravitons.
In the third (which is of interest here), they discuss why the dressing approach is needed.
They mention in a comment in the end of the paper the following:
Our results may have implications for the black hole information loss problem. Virtually all discussions of information loss in the black hole context rely on the possibility of localizing particles – from throwing a particle into a black hole to keeping information localized. We argued above that normalizable (and in particular localized) states are necessarily accompanied by soft radiation. It is well known that the absorption cross-section of radiation with frequency $\omega$ vanishes as $\omega\to 0$ and therefore it seems plausible that, whenever a localized particle is thrown into a black hole, the soft part of its state which is strongly correlated with the hard part remains outside the black hole. If this is true a black hole geometry is always in a mixed state which is purified by radiation outside the horizon.
If I understand where they are going they are basically saying the following:
Throwing a particle into a black hole requires one to consider a localized wavepacket as incoming state. By their arguments such a state is necessarily accompanied by a soft cloud of bosons. If the particle is not charged, it will be a soft cloud of gravitons. If it is charged it will be both a soft cloud of gravitons and photons.
By the soft factorization of the dynamics, the hard and soft parts of the state evolve independently. Hence the soft part cannot constrain the hard part. But anyway, it is established that the absorption cross section by the black hole vanishes as $\omega\to 0$.
Hence while the hard particle will cross the horizon, the soft cloud will be trapped outside.
Now, at least intuitively for me, these two results seem highly related.
In the first matter crossing the horizon excites soft bosons on the horizon. In this one, matter crosses the horizon and leaves upon it a soft cloud of soft bosons. The final effect is to end up with bosons added in the horizon whenever matter crosses the horizon.
So: are these two thing actually connected and if so how? Or are they just two distinct mechanisms, such that both occur when matter falls through the horizon?
I have the feeling (which may be totally wrong), that the second thing is actually the physical mechanism through which the first thing occurs.