The first 17 minutes or so are a very well done, but also very basic introduction to the black hole information loss problem. If you’re familiar with that, you can skip to 17:25. If you know the BMS group and only want to hear about the conserved charges on the horizon, skip to 45:00. Go to 56:10 for the summary.
Last week, there furthermore was a paper on the arxiv with a very similar argument: BMS invariance and the membrane paradigm, by Robert Penna from MIT, though this paper doesn’t directly address the information loss problem. One is lead to suspect that the author was working on the topic for a while, then heard about the idea put forward by Hawking and Perry and made sure to finish and upload his paper to the arxiv immediately... Towards the end of the paper the author also expresses concern, as I did earlier, that these degrees of freedom cannot possibly contain all the relevant information “This may be relevant for the information problem, as it forces the outgoing Hawking radiation to carry the same energy and momentum at every angle as the infalling state. This is usually not enough information to fully characterize an S-matrix state...”
The third person involved in this work is Andrew Strominger, who has been very reserved on the whole media hype. Eryn Brown reports for Phys.org
“Contacted via telephone Tuesday evening, Strominger said he felt confident that the information loss paradox was not irreconcilable. But he didn't think everything was settled just yet.(Did Hawking actually say that? Can someone point me to a source?)
He had heard Hawking say there would be a paper by the end of September. It had been the first he'd learned of it, he laughed, though he said the group did have a draft.”
Meanwhile I’ve pushed this idea back and forth in my head and, lacking further information about what they hope to achieve with this approach, have tentatively come to the conclusion that it can’t solve the problem. The reason is the following.
The endstate of black hole collapse is known to be simple and characterized only by three “hairs” – the mass, charge, and angular momentum of the black hole. This means that all higher multipole moments – deviations of the initial mass configuration from perfect spherical symmetry – have to be radiated off during collapse. If you disregard actual emission of matter, it will be radiated off in gravitons. The angular momentum related to these multipole moments has to be conserved, and there has to be an energy flux related to the emission. In my reading the BMS group and its conserved charges tell you exactly that: the multipole moments can’t vanish, they have to go to infinity. Alternatively you can interpret this as the black hole not actually being hair-less, if you count all that’s happned in the dynamical evolution.
Having said that, I didn’t know the BMS group before, but I never doubted this to be the case, and I don’t think anybody doubted this. But this isn’t the problem. The problem that occurs during collapse exists already classically, and is not in the multipole moments – which we know can’t get lost – it’s in the density profile in the radial direction. Take the simplest example: one shell of mass M, or two concentric shells of half the mass. The outside metric is identical. The inside metric vanishes behind the horizon. Where does the information about this distribution go if you let the shells collapse?
Now as Malcom said in his lecture, you can make a power-series expansion of the (Bondi) mass around the asymptotic value, and I’m pretty sure it contains the missing information about the density profile (which however already misses information of the quantum state). But this isn’t information you can measure locally, since you need an infinite amount of derivatives or infinite space to make your measurement respectively. And besides this, it’s not particularly insightful: If you have a metric that is analytic with an infinite convergence radius, you can expand it around any point and get back the metric in the whole space-time, including the radial profile. You don’t need any BMS group or conserved charges for that. (The example with the two shells is not analytical, it’s also pathological for various reasons.)
As an aside, that the real problem with the missing information in black hole collapse is in the radial direction and not in the angular direction is the main reason I never believed the strong interpretation of the Bekenstein-Hawking entropy. It seems to indicate that the entropy, which scales with the surface area, counts the states that are accessible from the outside and not all the states that black holes form from.
Feedback on this line of thought is welcome.
In summary, the Hawking-Perry argument makes perfect sense and it neatly fits together with all I know about black holes. But I don’t see how it gets one closer to solve the problem.