The variance of area fluctuations of a causal diamond in Minkowski spacetime is claimed to satisfy ⟨(ΔA)²⟩ ≥ (2πG/d)⟨A⟩, using quantized gravitational phase space on a stretched horizon.
BMS invariance and the membrane paradigm
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abstract
The Bondi-van der Burg-Metzner-Sachs (BMS) group is the asymptotic symmetry group of asymptotically flat spacetime. It is infinite dimensional and entails an infinite number of conservation laws. According to the black hole membrane paradigm, null infinity (in asymptotically flat spacetime) and black hole event horizons behave like fluid membranes. The fluid dynamics of the membrane is governed by an infinite set of symmetries and conservation laws. Our main result is to point out that the infinite set of symmetries and conserved charges of the BMS group and the membrane paradigm are the same. This relationship has several consequences. First, it sheds light on the physical interpretation of BMS conservation laws. Second, it generalizes the BMS conservation laws to arbitrary subregions of arbitrary null surfaces. Third, it clarifies the identification of the superrotation subgroup of the BMS group. We briefly comment on the black hole information problem.
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Quantum Area Fluctuations from Gravitational Phase Space
The variance of area fluctuations of a causal diamond in Minkowski spacetime is claimed to satisfy ⟨(ΔA)²⟩ ≥ (2πG/d)⟨A⟩, using quantized gravitational phase space on a stretched horizon.