Quantum Chaos and Unitary Black Hole Evaporation

TL;DR

This paper explores how quantum chaos influences black hole evaporation in holographic theories, showing that semiclassical gravity is valid for most observables but breaks down for certain transition amplitudes, highlighting the quantum nature of black holes.

Contribution

It provides a detailed analysis of quantum chaos effects on black hole states and their implications for the validity of semiclassical gravity in holographic duals.

Findings

Semiclassical gravity holds for smooth observables over many eigenstates.

Quantum corrections are exponentially suppressed by the entropy S.

Breakdown of semiclassical description occurs in transition amplitudes affecting unitarity.

Abstract

The formation and evaporation of small AdS black holes in a theory with a holographic dual is governed by the usual rules of quantum mechanics. The eigenstate thermalization hypothesis explains the validity of semiclassical gravity for local bulk observables and can be used to quantify the magnitude of quantum corrections to the semiclassical approximation. The holographic dual produces a basis of black hole states with finite energy width, and observables that are smooth functions on the classical phase space will self-average over a large number of energy eigenstates, exponential in the Bekenstein-Hawking entropy S, leading to results that are consistent with semiclassical gravity up to small corrections of order exp(-S/2). As expected, the semiclassical description breaks down for transition amplitudes that contribute to the unitary S matrix of the holographic theory.