# Emergent geometry from stochastic dynamics, or Hawking evaporation in M(atrix) theory

## TL;DR

This paper models M-theory black holes using chaotic matrix dynamics, revealing how spacetime geometry and Hawking evaporation emerge from microscopic quantum chaos, with implications for information loss and non-unitarity.

## Contribution

It introduces a microscopic, chaotic matrix model of black hole evaporation that links emergent geometry with non-unitary quantum effects.

## Key findings

- Event horizon physics is non-local at the Planck scale.
- Non-unitarity and information loss arise from averaging over chaotic dynamics.
- Emergence of spacetime geometry correlates with non-unitary processes.

## Abstract

We develop an microscopic model of the M-theory Schwarzschild black hole using the Banks-Fischler-Shenker-Susskind Matrix formulation of quantum gravity. The underlying dynamics is known to be chaotic, which allows us to use methods from Random Matrix Theory and non-equilibrium statistical mechanics to propose a coarse-grained bottom-up picture of the event horizon -- and the associated Hawking evaporation phenomenon. The analysis is possible due to a hierarchy between the various timescales at work. Event horizon physics is found to be non-local at the Planck scale, and we demonstrate how non-unitary physics and information loss arise from the process of averaging over the chaotic unitary dynamics. Most interestingly, we correlate the onset of non-unitarity with the emergence of spacetime geometry outside the horizon. We also write a mean field action for the evolution of qubits -- represented by polarization states of supergravity modes. This evolution is shown to have similarities to a recent toy model of black hole evaporation proposed by Osuga and Page -- a model aimed at developing a plausible no-firewall scenario.