Microcanonical Path Integrals and the Holography of small Black Hole Interiors

TL;DR

This paper introduces a microcanonical path integral approach to better understand the interiors of small black holes in AdS/CFT, revealing new dualities and entanglement properties.

Contribution

It develops a microcanonical path integral framework that highlights new saddle points and dualities for small black hole interiors in AdS/CFT.

Findings

Standard black hole extensions are dual to microcanonical thermofield double states.

Maximizing microcanonical entropy determines dominant saddles.

Quantum effects become significant at narrow energy ensembles.

Abstract

We use a microcanonical path integral closely related to that introduced by Brown and York in 1992 to add new entries to the AdS/CFT dictionary concerning the interiors of small black holes. Stationary points of such path integrals are also stationary points of more standard canonical-type path integrals with fixed boundary metric, but the condition for dominance is now maximizing Hubeny-Rangamani-Takayanagi entropy at fixed energy. As a result, such path integrals can bring to the fore saddles that fail to dominate in more familiar contexts. We use this feature to argue that the standard Kruskal-like two-sided extension of small AdS black holes with energy $E_0$ is dual to a microcanonical version of the thermofield double state for AdS black holes that maximize the microcanonical bulk entropy at this energy. We also comment on entanglement in such states and on quantum effects that become large when the energy-width of the microcanonical ensemble is sufficiently small.