Black hole holography and mean field evolution

TL;DR

This paper explores how holographic theories of black holes exhibit quantum chaos and argues for the existence of a mean field approximation that captures the evolution of typical black hole states, with implications for observers inside black holes and cosmological horizons.

Contribution

It introduces the idea that holographic black hole theories must have a mean field approximation valid near the scrambling time, supported by simple spin model examples.

Findings

Holographic black holes exhibit quantum chaos.

A mean field approximation can describe typical black hole states.

Implications for observers inside black holes and cosmological horizons.

Abstract

Holographic theories representing black holes are expected to exhibit quantum chaos. We argue if the laws of quantum mechanics are expected to hold for observers inside such black holes, then such holographic theories must have a mean field approximation valid for typical black hole states, and for timescales approaching the scrambling time. Using simple spin models as examples, we examine the predictions of such an approach for observers inside black holes, and more speculatively inside cosmological horizons.