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  • Open Access

Island of an acoustic black hole in Schwarzschild spacetime

Yu-Ye Cheng* and Jia-Rui Sun†

  • *Contact author: chengyy53@mail2.sysu.edu.cn
  • †Contact author: sunjiarui@mail.sysu.edu.cn
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Phys. Rev. D 113, 064030 – Published 16 March, 2026

DOI: https://doi.org/10.1103/k1gn-zbz2

Abstract

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

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Phys. Rev. D 113, 064030– Published 16 March, 2026
  • Received 15 December 2025
  • Accepted 20 February 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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