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  • Open Access

Nonsingular black holes as dark matter

Paul C. W. Davies*, Damien A. Easson†, and Phillip B. Levin‡

  • Department of Physics and Beyond Center for Fundamental Concepts in Science, Arizona State University, Tempe, Arizona 85287-1504, USA

  • *Contact author: paul.davies@asu.edu
  • †Contact author: easson@asu.edu
  • ‡Contact author: philliplevin@asu.edu
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Phys. Rev. D 111, 103512 – Published 9 May, 2025

DOI: https://doi.org/10.1103/PhysRevD.111.103512

Abstract

It is commonly assumed that low-mass primordial black holes cannot constitute a significant fraction of the dark matter in our universe due to their predicted short lifetimes from the conventional Hawking radiation and evaporation process. Assuming physical black holes are nonsingular—likely due to quantum gravity or other high-energy physics—we demonstrate that a large class of nonsingular black holes have finite evaporation temperatures. This can lead to slowly evaporating low-mass black holes or to remnant mass states that circumvent traditional evaporation constraints. As a proof of concept, we explore the limiting curvature hypothesis and the evaporation process of a nonsingular black hole solution in two-dimensional dilaton gravity. We identify generic features of the radiation profile and compare them with known regular black holes, such as the Bardeen solution in four dimensions. Remnant masses are proportional to the fundamental length scale, and we argue that slowly evaporating low-mass nonsingular black holes, or remnants, are viable dark matter candidates.

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References (64)

  1. F. Zwicky, Die Rotverschiebung von extragalaktischen Nebeln, Helv. Phys. Acta 6, 110 (1933).
  2. V. C. Rubin, N. Thonnard, and W. K. Ford, Jr., Rotational properties of 21 SC galaxies with a large range of luminosities and radii, from NGC 4605 (R = 4 kpc) to UGC 2885 (R = 122 kpc), Astrophys. J. 238, 471 (1980).
  3. T. M. C. Abbott et al. (DES Collaboration), Dark energy survey year 3 results: Constraints on extensions to ΛCDM with weak lensing and galaxy clustering, Phys. Rev. D 107, 083504 (2023).
  4. K. M. Belotsky, A. D. Dmitriev, E. A. Esipova, V. A. Gani, A. V. Grobov, M. Yu. Khlopov, A. A. Kirillov, S. G. Rubin, and I. V. Svadkovsky, Signatures of primordial black hole dark matter, Mod. Phys. Lett. A 29, 1440005 (2014).
  5. Anne M. Green and Bradley J. Kavanagh, Primordial black holes as a dark matter candidate, J. Phys. G 48, 043001 (2021).
  6. Pablo Villanueva-Domingo, Olga Mena, and Sergio Palomares-Ruiz, A brief review on primordial black holes as dark matter, Front. Astron. Space Sci. 8, 87 (2021).
  7. Bernard J. Carr and Anne M. Green, The history of primordial black holes, arXiv:2406.05736.
  8. S. W. Hawking, Black hole explosions, Nature (London) 248, 30 (1974).
  9. Bradley J. Kavanagh, bradkav/pbhbounds: Release version (2019), 10.5281/zenodo.3538999.
  10. Joseph Polchinski, The black hole information problem, in Theoretical Advanced Study Institute in Elementary Particle Physics: New Frontiers in Fields and Strings (2017), pp. 353–397, .
  11. Y. Aharonov, A. Casher, and S. Nussinov, The unitarity puzzle and Planck mass stable particles, Phys. Lett. B 191, 51 (1987).
  12. Jane H. MacGibbon, Can Planck-mass relics of evaporating black holes close the universe?, Nature (London) 329, 308 (1987).
  13. J. D. Barrow, Thermodynamics of open universes, Phys. Rev. D 46, R3227 (1992).
  14. John D. Barrow, Edmund J. Copeland, and Andrew R. Liddle, The cosmology of black hole relics, Phys. Rev. D 46, 645 (1992).
  15. Ronald J. Adler, Pisin Chen, and David I. Santiago, The generalized uncertainty principle and black hole remnants, Gen. Relativ. Gravit. 33, 2101 (2001).
  16. Damien A. Easson, Hawking radiation of nonsingular black holes in two-dimensions, J. High Energy Phys. 02 (2003) 037.
  17. Pisin Chen and Ronald J. Adler, Black hole remnants and dark matter, Nucl. Phys. B, Proc. Suppl. 124, 103 (2003).
  18. Yi-Fu Cai and Damien A. Easson, Black holes in an asymptotically safe gravity theory with higher derivatives, J. Cosmol. Astropart. Phys. 09 (2010) 002.
  19. Irina Dymnikova and Maxim Khlopov, Regular black hole remnants and graviatoms with de Sitter interior as heavy dark matter candidates probing inhomogeneity of early universe, Int. J. Mod. Phys. D 24, 1545002 (2015).
  20. Bernard Carr and Florian Kuhnel, Primordial black holes as dark matter candidates, SciPost Phys. Lect. Notes 48, 1 (2022).
  21. Stefano Profumo, Ultralight primordial black holes, arXiv:2405.00546.
  22. Marco Calzà, Davide Pedrotti, and Sunny Vagnozzi, Primordial regular black holes as all the dark matter. I. Time-radial-symmetric metrics, Phys. Rev. D 111, 024009 (2025).
  23. Marco Calzà, Davide Pedrotti, and Sunny Vagnozzi, Primordial regular black holes as all the dark matter. II. Non-time-radial-symmetric and loop quantum gravity-inspired metrics, Phys. Rev. D 111, 024010 (2025).
  24. Damien A. Easson, Nonsingular Schwarzschild–de Sitter black hole, Classical Quantum Gravity 35, 235005 (2018).
  25. M. A. Markov, Maximal curvature conjecture, JETP Lett. 36, 265 (1982), http://jetpletters.ru/ps/1334/article_20160.pdf.
  26. Damien A. Easson, The accelerating universe and a limiting curvature proposal, J. Cosmol. Astropart. Phys. 02 (2007) 004.
  27. S. M. Christensen and S. A. Fulling, Trace anomalies and the Hawking effect, Phys. Rev. D 15, 2088 (1977).
  28. F. Grard, and J. Nuyts, Kaluza-Klein towers for spinors in warped spaces, Phys. Rev. D 79, 064019 (2009).
  29. S. Deser, M. J. Duff, and C. J. Isham, Nonlocal conformal anomalies, Nucl. Phys. B111, 45 (1976).
  30. Surjeet Rajendran, New directions in the search for dark matter, SciPost Phys. Lect. Notes 56, 1 (2022).
  31. James M. Bardeen, in Proceedings of the 5th International Conference on General Relativity and Gravitation (GR5), Tbilisi, USSR, 1968 (Publishing House of the Academy of Sciences of the Georgian SSR, Tbilisi, 1968).
  32. Sean A. Hayward, Formation and evaporation of regular black holes, Phys. Rev. Lett. 96, 031103 (2006).
  33. Zhong-Ying Fan and Xiaobao Wang, Construction of regular black holes in general relativity, Phys. Rev. D 94, 124027 (2016).
  34. I. Dymnikova, Vacuum nonsingular black hole, Gen. Relativ. Gravit. 24, 235 (1992).
  35. Anne M. Green, Primordial black holes as a dark matter candidate—a brief overview, Nucl. Phys. B1003, 116494 (2024).
  36. Bernard J. Carr, The primordial black hole mass spectrum, Astrophys. J. 201, 1 (1975).
  37. Jane H. MacGibbon and Bernard J. Carr, Cosmic rays from primordial black holes, Astrophys. J. 371, 447 (1991).
  38. B. J. Carr, Kazunori Kohri, Yuuiti Sendouda, and Jun’ichi Yokoyama, New cosmological constraints on primordial black holes, Phys. Rev. D 81, 104019 (2010).
  39. Ranjan Laha, Primordial black holes as a dark matter candidate are severely constrained by the Galactic Center 511 keV γ -ray line, Phys. Rev. Lett. 123, 251101 (2019).
  40. Mathieu Boudaud and Marco Cirelli, Voyager 1  e± further constrain primordial black holes as dark matter, Phys. Rev. Lett. 122, 041104 (2019).
  41. Damien A. Easson and Robert H. Brandenberger, Universe generation from black hole interiors, J. High Energy Phys. 06 (2001) 024.
  42. S. W. Hawking and R. Penrose, The singularities of gravitational collapse and cosmology, Proc. R. Soc. A 314, 529 (1970).
  43. O. B. Zaslavskii, Regular black holes and energy conditions, Phys. Lett. B 688, 278 (2010).
  44. Hideki Maeda, Quest for realistic non-singular black-hole geometries: Regular-center type, J. High Energy Phys. 11 (2022) 108.
  45. G. D. Birkhoff, Relativity and Modern Physics (Harvard University Press, Cambridge, MA, 1923), p. 253.
  46. Damien A. Easson and Max W. Pezzelle, Kleinian black holes, Phys. Rev. D 109, 044007 (2024).
  47. Saugata Chatterjee, Damien A. Easson, and Maulik Parikh, Energy conditions in the Jordan frame, Classical Quantum Gravity 30, 235031 (2013).
  48. Roger Penrose, Gravitational collapse and space-time singularities, Phys. Rev. Lett. 14, 57 (1965).
  49. Stephen Hawking, The occurrence of singularities in cosmology, Proc. R. Soc. A 294, 511 (1966).
  50. Stephen Hawking, The occurrence of singularities in cosmology. II, Proc. R. Soc. A 295, 490 (1966).
  51. Stephen Hawking, The occurrence of singularities in cosmology. III. Causality and singularities, Proc. R. Soc. A 300, 187 (1967).
  52. J. E. Lesnefsky, D. A. Easson, and P. C. W. Davies, Past-completeness of inflationary spacetimes, Phys. Rev. D 107, 044024 (2023).
  53. Damien A. Easson and Joseph E. Lesnefsky, Inflationary resolution of the initial singularity, arXiv:2402.13031.
  54. Damien A. Easson and Joseph E. Lesnefsky, Eternal universes, arXiv:2404.03016.
  55. S. W. Hawking and G. F. R. Ellis, The Large Scale Structure (Cambridge University Press, Cambridge UK, 1973).
  56. Damien A. Easson, Cynthia Keeler, and Tucker Manton, Classical double copy of nonsingular black holes, Phys. Rev. D 102, 086015 (2020).
  57. Eloy Ayon-Beato and Alberto Garcia, Regular black hole in general relativity coupled to nonlinear electrodynamics, Phys. Rev. Lett. 80, 5056 (1998).
  58. Eloy Ayon-Beato and Alberto Garcia, The Bardeen model as a nonlinear magnetic monopole, Phys. Lett. B 493, 149 (2000).
  59. Patricio Gaete, Kimet Jusufi, and Piero Nicolini, Charged black holes from T-duality, Phys. Lett. B 835, 137546 (2022).
  60. Pablo Bueno, Pablo A. Cano, Robie A. Hennigar, and Ángel J. Murcia, Dynamical formation of regular black holes, arXiv:2412.02742.
  61. Pablo Bueno, Pablo A. Cano, Robie A. Hennigar, and Ángel J. Murcia, Regular black holes from thin-shell collapse, arXiv:2412.02740.
  62. Sheng-Feng Yan, Chunlong Li, Lingqin Xue, Xin Ren, Yi-Fu Cai, Damien A. Easson, Ye-Fei Yuan, and Hongsheng Zhao, Testing the equivalence principle via the shadow of black holes, Phys. Rev. Res. 2, 023164 (2020).
  63. Leonardo Balart, Grigoris Panotopoulos, and Ángel Rincón, On new regular charged black hole solutions: Limiting curvature condition, quasinormal modes and shadows, Ann. Phys. (Amsterdam) 473, 169865 (2025).
  64. Vitalii Vertogradov, Ali Övgün, and Daniil Shatov, Formation of regular black hole from baryonic matter, arXiv:2502.00521.

Outline

Information

Phys. Rev. D 111, 103512– Published 9 May, 2025
  • Received 4 November 2024
  • Accepted 28 April 2025
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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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