Probing Hawking radiation through capacity of entanglement

TL;DR

This paper investigates the capacity of entanglement as a diagnostic tool for understanding gravitational phase transitions and black hole evaporation, revealing peaks and discontinuities associated with different phases.

Contribution

It introduces the capacity of entanglement as a new diagnostic for gravitational phase transitions and black hole evaporation, linking it to replica wormhole geometries and island formation.

Findings

Capacity peaks around the Page time indicating phase transition.

Discontinuities in capacity signal saddle switches and island formation.

Capacity serves as an effective diagnostic for black hole evaporation processes.

Abstract

We consider the capacity of entanglement in models related with the gravitational phase transitions. The capacity is labeled by the replica parameter which plays a similar role to the inverse temperature in thermodynamics. In the end of the world brane model of a radiating black hole the capacity has a peak around the Page time indicating the phase transition between replica wormhole geometries of different types of topology. Similarly, in a moving mirror model describing Hawking radiation the capacity typically shows a discontinuity when the dominant saddle switches between two phases, which can be seen as a formation of island regions. In either case we find the capacity can be an invaluable diagnostic for a black hole evaporation process.