- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Quantization of black hole entropy for black holes in subtracted geometry

Mirjam Cvetič*

Malcolm J. Perry†

  • Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA; Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA; and Center for Applied Mathematics and Theoretical Physics, University of Maribor, Maribor, Slovenia

  • *Contact author: cvetic@physics.upenn.edu
  • †Contact author: mjp1@cam.ac.uk
PDF

Phys. Rev. D 113, 046018 – Published 24 February, 2026

DOI: https://doi.org/10.1103/bgls-r3rw

Abstract

We carefully examine the exact analytic spectrum of quasinormal modes of general black holes in the so-called subtracted geometry of maximally supersymmetric supergravity. These black holes have the same area and surface gravity at both the outer and inner horizons as asymptotically flat Kerr black holes. We proceed to explore the relationship with conformal field theories that describe horizon physics of these black holes. As a consequence, we show that it is consistent to view the horizon area of these black holes as being quantized in units of 8πlPl2.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (48)

  1. S. W. Hawking, Particle creation by black holes, Commun. Math. Phys. 43, 199 (1975); 46, 206(E) (1976).
  2. J. D. Bekenstein, Black holes and the second law, Lett. Nuovo Cimento 4, 737 (1972).
  3. J. D. Bekenstein, Black holes and entropy, Phys. Rev. D 7, 2333 (1973).
  4. L. Boltzmann, Über die Beziehung eines allgemeine mechanischen Satzes zum zweiten Haupsatze der Wärmetheorie, Sitzungber. Kais. Akad. Wiss. Math. Naturwiss. Cl. Abt II 67, 373 (1877).
  5. J. A. Wheeler, Information, physics, quantum: The search for links, in Proceedings of the Third International Symposium on the Foundations of Quantum Mechanics, edited by (Physical Society of Japan, Tokyo, 1990).
  6. G. ’t Hooft, The black hole interpretation of string theory, Nucl. Phys. B335, 138 (1990).
  7. L. Susskind, The world as a hologram, J. Math. Phys. (N.Y.) 36, 6377 (1995).
  8. J. D. Bekenstein, The quantum mass spectrum of the Kerr black hole, Lett. Nuovo Cimento 11, 467 (1974).
  9. V. F. Mukhanov, Are black holes quantized?, JETP Lett. 44, 63 (1986).
  10. J. D. Bekenstein and V. F. Mukhanov, Spectroscopy of the quantum black hole, Phys. Lett. B 360, 7 (1995).
  11. S. Hod, Bohr’s correspondence principle and the area spectrum of quantum black holes, Phys. Rev. Lett. 81, 4293 (1998).
  12. M. Maggiore, The physical interpretation of the spectrum of black hole quasinormal modes, Phys. Rev. Lett. 100, 141301 (2008).
  13. A. J. M. Medved, On the Kerr quantum area spectrum, Classical Quantum Gravity 25, 205014 (2008).
  14. A. Castro, A. Maloney, and A. Strominger, Hidden conformal symmetry of the Kerr black hole, Phys. Rev. D 82, 024008 (2010).
  15. M. Cvetič and F. Larsen, Conformal symmetry for black holes in four dimensions, J. High Energy Phys. 09 (2012) 076.
  16. M. Cvetič and G. W. Gibbons, Conformal symmetry of a black hole as a scaling limit: A black hole in an asymptotically conical box, J. High Energy Phys. 07 (2012) 014.
  17. M. Cvetič and G. W. Gibbons, Exact quasinormal modes for the near horizon Kerr metric, Phys. Rev. D 89, 064057 (2014).
  18. M. Cvetič, G. W. Gibbons, and Z. H. Saleem, Quasinormal modes for subtracted rotating and magnetized geometries, Phys. Rev. D 90, 124046 (2014).
  19. M. Cvetič, G. W. Gibbons, and Z. H. Saleem, Thermodynamics of asymptotically conical geometries, Phys. Rev. Lett. 114, 231301 (2015).
  20. O. S. An, M. Cvetič, and I. Papadimitriou, Black hole thermodynamics from a variational principle: Asymptotically conical backgrounds, J. High Energy Phys. 03 (2016) 086.
  21. M. Cvetič and D. Youm, Entropy of nonextreme charged rotating black holes in string theory, Phys. Rev. D 54, 2612 (1996).
  22. Z. W. Chong, M. Cvetič, H. Lu, and C. N. Pope, Charged rotating black holes in four-dimensional gauged and ungauged supergravities, Nucl. Phys. B717, 246 (2005).
  23. M. Cvetič, G. W. Gibbons, H. Lü, and C. N. Pope, Killing horizons: Negative temperatures and entropy super-additivity, Phys. Rev. D 98, 106015 (2018).
  24. D. Frenkel and P. B. Warren, Gibbs, Boltzmann, and negative temperatures, Am. J. Phys. 83, 163 (2015).
  25. M. Cvetič and F. Larsen, Grey body factors for rotating black holes in four-dimensions, Nucl. Phys. B506, 107 (1997).
  26. A. Strominger, Black hole entropy from near horizon microstates, J. High Energy Phys. 02 (1998) 009.
  27. M. Cvetič and F. Larsen, Greybody factors and charges in Kerr/CFT, J. High Energy Phys. 09 (2009) 088.
  28. A. Castro, J. M. Lapan, A. Maloney, and M. J. Rodriguez, Black hole scattering from monodromy, Classical Quantum Gravity 30, 165005 (2013).
  29. A. Castro, J. M. Lapan, A. Maloney, and M. J. Rodriguez, Black hole monodromy and conformal field theory, Phys. Rev. D 88, 044003 (2013).
  30. S. Haco, S. W. Hawking, M. J. Perry, and A. Strominger, Black hole entropy and soft hair, J. High Energy Phys. 12 (2018) 098.
  31. G. W. Gibbons and M. J. Perry, Black holes and thermal Green’s functions, Proc. R. Soc. A 358, 467 (1978).
  32. C. V. Vishveshwara, Scattering of gravitational radiation by a Schwarzschild black-hole, Nature (London) 227, 936 (1970).
  33. S. Chandrasekhar and S. L. Detweiler, The quasi-normal modes of the Schwarzschild black hole, Proc. R. Soc. A 344, 441 (1975).
  34. E. W. Leaver, An analytic representation for the quasi normal modes of Kerr black holes, Proc. R. Soc. A 402, 285 (1985).
  35. E. W. Leaver, Spectral decomposition of the perturbation response of the Schwarzschild geometry, Phys. Rev. D 34, 384 (1986).
  36. H.-P. Nollert and B. G. Schmidt, Quasinormal modes of Schwarzschild black holes: Defined and calculated via Laplace transformation, Phys. Rev. D 45, 2617 (1992).
  37. H.-P. Nollert, Quasinormal modes of Schwarzschild black holes: The determination of quasinormal frequencies with very large imaginary parts, Phys. Rev. D 47, 5253 (1993).
  38. H.-P. Nollert, Quasinormal modes: The characteristic “sound” of black holes and neutron stars, Classical Quantum Gravity 16, R159 (1999).
  39. K. D. Kokkotas and B. G. Schmidt, Quasinormal modes of stars and black holes, Living Rev. Relativity 2, 2 (1999).
  40. L. Motl and A. Neitzke, Asymptotic black hole quasinormal frequencies, Adv. Theor. Math. Phys. 7, 307 (2003).
  41. V. Ferrari and L. Gualtieri, Quasi-normal modes and gravitational wave astronomy, Gen. Relativ. Gravit. 40, 945 (2008).
  42. E. Berti, V. Cardoso, and A. O. Starinets, Quasinormal modes of black holes and black branes, Classical Quantum Gravity 26, 163001 (2009).
  43. R. A. Konoplya and A. Zhidenko, Quasinormal modes of black holes: From astrophysics to string theory, Rev. Mod. Phys. 83, 793 (2011).
  44. B. Carneiro da Cunha and F. Novaes, Kerr scattering coefficients via isomonodromy, J. High Energy Phys. 11 (2015) 144.
  45. B. Carneiro da Cunha and J. P. Cavalcante, Confluent conformal blocks and the Teukolsky master equation, Phys. Rev. D 102, 105013 (2020).
  46. G. Aminov, A. Grassi, and Y. Hatsuda, Black hole quasinormal modes and Seiberg–Witten theory, Ann. Henri Poincare 23, 1951 (2022).
  47. G. Bonelli, C. Iossa, D. P. Lichtig, and A. Tanzini, Exact solution of Kerr black hole perturbations via CFT2 and instanton counting: Greybody factor, quasinormal modes, and Love numbers, Phys. Rev. D 105, 044047 (2022).
  48. S. W. Hawking, Breakdown of predictability in gravitational collapse, Phys. Rev. D 14, 2460 (1976).

Outline

Information

Phys. Rev. D 113, 046018– Published 24 February, 2026
  • Received 30 April 2025
  • Accepted 26 January 2026
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation