Microstructure in matrix elements

TL;DR

This paper models black hole evaporation by extending a simple matrix model to include interior dynamics and EOW branes, revealing how strong coupling leads to non-random states and deviations from thermality.

Contribution

It introduces a model incorporating interior dynamics and EOW branes to study Hawking radiation, showing the importance of strong coupling effects without ensemble averaging.

Findings

EOW states become non-random at strong coupling

Density matrix deviates from thermal state with off-diagonal fluctuations

All Renyi entropies have a derived analytic formula

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.