I would like to discuss a bit this paper (http://arxiv.org/abs/1508.06577):(adsbygoogle = window.adsbygoogle || []).push({});

BMS invariance and the membrane paradigm

Robert F. Penna

(Submitted on 26 Aug 2015)

We reinterpret the BMS invariance of gravitational scattering using the membrane paradigm. BMS symmetries imply an infinite number of conserved quantities. Energy conservation at every angle is equivalent to the fluid energy equation on the membrane (a conservation law at each point in the fluid). Momentum conservation at every angle is equivalent to the Damour-Navier-Stokes equation on the membrane. Soft gravitons are encoded in the membrane's mass-energy density, Σ(z,z¯). Fluid dynamics is governed by infinite dimensional reparametrization invariance, which corresponds to the group of volume preserving diffeomorphisms. This coincides with the generalized BMS group, so there is a connection between the fluid and gravity pictures at the level of symmetries. The existence of membrane fluid conservation laws at event horizons implies BMS symmetries also act on event horizons. This may be relevant for the information problem because it implies infalling information can be stored in Σ(z,z¯) at the horizon. The teleological nature of the membrane at the horizon may be related to the black hole final state proposal.

I think it is related to the recent idea sketch reported by Hawking-Perry-Strominger.

To me it appears that the paper has two parts. First, a technical discussion of BMS-like symmetries on black hole horizons in flat space. Second, a brief speculation about how the technical part might relate to the black hole information paradox. My impression is that the HPS idea is in roughly the same state, but we haven't really seen a proper presentation of the HPS idea so I'll focus on Penna's work.

Some questions I would like to understand:

1. Since Penna is proposing that there is a conservation law for every angle, it seems to me that any information stored in this BMS-like data would not scramble much or at all (see e.g. http://arxiv.org/abs/0708.4025 and http://arxiv.org/abs/0808.2096). Is this right?

2. It doesn't seem quantum enough. How can the quantum state of an infalling qubit be encoded in the classical BMS data? There also doesn't seem to be enough of it.

3. In AdS things should work slightly differently. Penna observes that the fluid on the horizon doesn't conduct heat which is why one has an infinite number of conservation laws. But in AdS/CFT the dual field theory hydrodynamics does conduct heat, so are these extra symmetries not present in that case? Is the problem the cosmological constant?

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# BMS symmetries and black hole horizons

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