Island of acoustic black hole in Schwarzschild spacetime

TL;DR

This paper investigates the entanglement entropy of phonons in acoustic black holes derived from Schwarzschild spacetime, demonstrating the emergence of the Page curve and insights into unitarity and causal structure in analogue gravity systems.

Contribution

It applies the island formula to acoustic black holes in Schwarzschild spacetime, analyzing entanglement entropy in both non-extremal and extremal cases, revealing new aspects of information paradox resolution.

Findings

Page curve emerges in non-extremal case

Entanglement entropy proportional to horizon area at late times

Divergence of entropy in extremal case

Abstract

We study an analogue information paradox in acoustic black holes which are emerged from the superfluid surrounding a Schwarzschild black hole. The resulting acoustic black hole contains both acoustic horizons and optical horizon, with analogue Hawking radiation, i.e. phonons, emitted from the outer acoustic horizon. By using the island formula, we calculate the entanglement entropy of analogue Hawking radiation of the acoustic black hole in both non-extremal and extremal cases. In the non-extremal case, the entanglement entropy of phonons follow the Page curve due to the emergence of islands, and it is approximately proportional to the area of the acoustic horizon at late time. While in the extremal case, the entanglement entropy of phonons diverges, leading to an ill-defined Page time. Our study verifies the unitarity of the analogue gravity system, and provides further insight into the connection between the entanglement entropy and the causal structure of spacetime.