Microstructure in matrix elements

Abstract

We investigate the simple model of Pennington, Shenker, Stanford and Yang for modeling the density matrix of Hawking radiation, but further include dynamics for EOW branes behind the horizon. This allows interactions that scatter one interior state to another, and also allows EOW loops. At strong coupling, we find that EOW states are no longer random; the ensemble has collapsed, and coupling constants encode the microscopic matrix elements of Hawking radiation. This suggests strong interior dynamics are important for understanding evaporating black holes, without any ensemble average. In this concrete model the density matrix of the radiation deviates from the thermal state, small off-diagonal fluctuations encode equivalences between naively orthogonal states, and bound the entropy from above. For almost evaporated black holes the off-diagonal terms become as large as the diagonal ones, eventually giving a pure state. We also find the unique analytic formula for all Renyi entropies.

30 pages + appendices; v2: updated acknowledgements

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• Page curve from dynamical branes in JT gravity
• Non-Isometric Quantum Error Correction in Gravity
• Branes in JT (super)gravity from group theory
• Quantum group origins of edge states in double-scaled SYK
• Baby universes, ensemble averages and factorizations with matters
• Product of Random States and Spatial (Half-)Wormholes