Islands and Uhlmann phase: Explicit recovery of classical information from evaporating black holes

TL;DR

This paper presents a protocol enabling an observer to explicitly recover classical information from an evaporating black hole by measuring the Uhlmann phase of Hawking radiation, linking the black hole's interior phase space to initial matter configurations.

Contribution

It introduces a practical method to recover classical information from black holes using the Uhlmann phase, assuming replica wormholes influence the gravitational path integral.

Findings

Classical information can be explicitly reconstructed from Hawking radiation.

The phase space of the black hole interior is recoverable via the Uhlmann phase.

The process establishes an invertible map between initial matter and black hole interior.

Abstract

Recent work has established a route towards the semiclassical validity of the Page curve, and so provided evidence that information escapes an evaporating black hole. However, a protocol to explicitly recover and make practical use of that information in the classical limit has not yet been given. In this paper, we describe such a protocol, showing that an observer may reconstruct the phase space of the black hole interior by measuring the Uhlmann phase of the Hawking radiation. The process of black hole formation and evaporation provides an invertible map between this phase space and the space of initial matter configurations. Thus, all classical information is explicitly recovered. We assume in this paper that replica wormholes contribute to the gravitational path integral.