Asymmetric interiors for small black holes

TL;DR

This paper develops a CFT-based framework to understand the interior of small black holes, showing how infalling observers experience classical geometry and how entanglement breakdown affects outgoing fields in evaporating black holes.

Contribution

It introduces a representation of bulk fields in the CFT that captures the black hole interior and analyzes the impact of entanglement dynamics on the outgoing field description.

Findings

Ingoing fields have simple CFT representations even inside small black holes.

Classical infalling observers experience the classical geometry in the interior.

Entanglement breakdown at the Page time affects the outgoing field's local geometry representation.

Abstract

We develop the representation of infalling observers and bulk fields in the CFT as a way to understand the black hole interior in AdS. We first discuss properties of CFT states which are dual to black holes. We then show that in the presence of a Killing horizon bulk fields can be decomposed into pieces we call ingoing and outgoing. The ingoing field admits a simple operator representation in the CFT, even inside a small black hole at late times, which leads to a simple CFT description of infalling geodesics. This means classical infalling observers will experience the classical geometry in the interior. The outgoing piece of the field is more subtle. In an eternal two-sided geometry it can be represented as an operator on the left CFT. In a stable one-sided geometry it can be described using entanglement via the PR construction. But in an evaporating black hole trans-horizon entanglement breaks down at the Page time, which means that for old black holes the PR construction fails and the outgoing field does not see local geometry. This picture of the interior allows the CFT to reconcile unitary Hawking evaporation with the classical experience of infalling observers.