Replica Wormholes and the Entropy of Hawking Radiation

TL;DR

This paper demonstrates that including replica wormholes in gravitational path integrals resolves the black hole information paradox by reproducing the island rule for entropy in a semi-classical setting.

Contribution

It introduces the concept of replica wormholes as new saddle points that fix the entropy discrepancy in black hole evaporation, providing a semi-classical derivation of the island rule.

Findings

Replica wormholes appear as complex saddles in the gravitational path integral.

Inclusion of wormholes reproduces the island rule for entropy.

The approach is explicitly demonstrated in Jackiw-Teitelboim gravity.

Abstract

The information paradox can be realized in anti-de Sitter spacetime joined to a Minkowski region. In this setting, we show that the large discrepancy between the von Neumann entropy as calculated by Hawking and the requirements of unitarity is fixed by including new saddles in the gravitational path integral. These saddles arise in the replica method as complexified wormholes connecting different copies of the black hole. As the replica number $n \to 1$, the presence of these wormholes leads to the island rule for the computation of the fine-grained gravitational entropy. We discuss these replica wormholes explicitly in two-dimensional Jackiw-Teitelboim gravity coupled to matter.