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Evolving Page curves for black holes coupled to cooling baths

Waheed A. Dar*

Nirmalya Kajuri

Rinkesh Panigrahi

  • *Contact author: waheed.dar1729@gmail.com
  • Contact author: nirmalya@iitmandi.ac.in
  • Contact author: d23189@students.iitmandi.ac.in

Phys. Rev. D 113, 106001 – Published 5 May, 2026

DOI: https://doi.org/10.1103/28wh-w9db

Abstract

We consider scenarios where Jackiw-Teitelboim black holes are attached to baths whose temperatures can be manipulated externally. We consider the bath to be cooled continuously and numerically investigate the subsequent evolution of the generalized entropies of the black hole. Page curves corresponding to several different cooling profiles of the bath are obtained.

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References (33)

  1. Don N. Page, Average entropy of a subsystem, Phys. Rev. Lett. 71, 1291 (1993).
  2. Ahmed Almheiri, Netta Engelhardt, Donald Marolf, and Henry Maxfield, The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole, J. High Energy Phys. 12 (2019) 063.
  3. Geoffrey Penington, Entanglement wedge reconstruction and the information paradox, J. High Energy Phys. 09 (2020) 002.
  4. Ahmed Almheiri, Raghu Mahajan, Juan Maldacena, and Ying Zhao, The Page curve of Hawking radiation from semiclassical geometry, J. High Energy Phys. 03 (2020) 149.
  5. Netta Engelhardt and Aron C. Wall, Quantum extremal surfaces: Holographic entanglement entropy beyond the classical regime, J. High Energy Phys. 01 (2015) 073.
  6. Geoff Penington, Stephen H. Shenker, Douglas Stanford, and Zhenbin Yang, Replica wormholes and the black hole interior, J. High Energy Phys. 03 (2022) 205.
  7. Ahmed Almheiri, Thomas Hartman, Juan Maldacena, Edgar Shaghoulian, and Amirhossein Tajdini, Replica wormholes and the entropy of Hawking radiation, J. High Energy Phys. 05 (2020) 013.
  8. Ahmed Almheiri, Thomas Hartman, Juan Maldacena, Edgar Shaghoulian, and Amirhossein Tajdini, The entropy of Hawking radiation, Rev. Mod. Phys. 93, 035002 (2021).
  9. Ahmed Almheiri, Raghu Mahajan, and Juan Maldacena, Islands outside the horizon, arXiv:1910.11077.
  10. Donald Marolf and Henry Maxfield, Transcending the ensemble: Baby universes, spacetime wormholes, and the order and disorder of black hole information, J. High Energy Phys. 08 (2020) 044.
  11. Ahmed Almheiri, Raghu Mahajan, and Jorge E. Santos, Entanglement islands in higher dimensions, SciPost Phys. 9, 001 (2020).
  12. Hong Zhe Chen, Robert C. Myers, Dominik Neuenfeld, Ignacio A. Reyes, and Joshua Sandor, Quantum extremal islands made easy, part I: Entanglement on the brane, J. High Energy Phys. 10 (2020) 166.
  13. Koji Hashimoto, Norihiro Iizuka, and Yoshinori Matsuo, Islands in Schwarzschild black holes, J. High Energy Phys. 06 (2020) 085.
  14. Thomas Hartman, Yikun Jiang, and Edgar Shaghoulian, Islands in cosmology, J. High Energy Phys. 11 (2020) 111.
  15. Fridrik Freyr Gautason, Lukas Schneiderbauer, Watse Sybesma, and Larus Thorlacius, Page curve for an evaporating black hole, J. High Energy Phys. 05 (2020) 091.
  16. Vijay Balasubramanian, Arjun Kar, and Tomonori Ugajin, Islands in de Sitter space, J. High Energy Phys. 02 (2021) 072.
  17. Chethan Krishnan, Critical islands, J. High Energy Phys. 01 (2021) 179.
  18. Chethan Krishnan, Vaishnavi Patil, and Jude Pereira, Page Curve and the Information Paradox in Flat Space, 2020.
  19. Yi Ling, Yuxuan Liu, and Zhuo-Yu Xian, Island in charged black holes, J. High Energy Phys. 03 (2021) 251.
  20. Byoungjoon Ahn, Sang-Eon Bak, Hyun-Sik Jeong, Keun-Young Kim, and Ya-Wen Sun, Islands in charged linear dilaton black holes, Phys. Rev. D 105, 046012 (2022).
  21. Mariano Cadoni and Andrea Pierfrancesco Sanna, Unitarity and page curve for evaporation of 2D AdS black holes, Entropy 24, 101 (2021).
  22. Timothy J. Hollowood and S. Prem Kumar, Islands and Page curves for evaporating black holes in JT gravity, J. High Energy Phys. 08 (2020) 094.
  23. R. Jackiw, Lower dimensional gravity, Nucl. Phys. B252, 343 (1985).
  24. C. Teitelboim, Gravitation and Hamiltonian structure in two space-time dimensions, Phys. Lett. 126B, 41 (1983).
  25. Juan Maldacena and Douglas Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D 94, 106002 (2016).
  26. Ahmed Almheiri and Joseph Polchinski, Models of AdS2 backreaction and holography, J. High Energy Phys. 11 (2015) 014.
  27. Kristan Jensen, Chaos in AdS2 holography, Phys. Rev. Lett. 117, 111601 (2016).
  28. Juan Maldacena, Douglas Stanford, and Zhenbin Yang, Conformal symmetry and its breaking in two dimensional nearly anti-de-Sitter space, Prog. Theor. Exp. Phys. 2016, 12C104 (2016).
  29. Julius Engelsöy, Thomas G. Mertens, and Herman Verlinde, An investigation of AdS2 backreaction and holography, J. High Energy Phys. 07 (2016) 139.
  30. Thomas G. Mertens and Gustavo J. Turiaci, Solvable models of quantum black holes: A review on Jackiw–Teitelboim gravity, Living Rev. Relativity 26, 4 (2023).
  31. Thomas G. Mertens, Towards black hole evaporation in Jackiw-Teitelboim gravity, J. High Energy Phys. 07 (2019) 097.
  32. Pasquale Calabrese and John L. Cardy, Entanglement entropy and quantum field theory, J. Stat. Mech. (2004) P06002.
  33. https://github.com/rinkeshpanigrahi/Black-hole-evaporation.

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