- Open Access
Regular black holes from Oppenheimer-Snyder collapse
Phys. Rev. D 112, 064039 – Published 15 September, 2025
DOI: https://doi.org/10.1103/qrbb-mdvm
Abstract
It has been recently shown that regular black holes arise as the unique spherically symmetric solutions of broad families of generalizations of Einstein gravity involving infinite towers of higher-curvature corrections in spacetime dimensions. In this paper we argue that such regular black holes arise as the byproduct of the gravitational collapse of pressureless dust stars. We show that, just like for Einstein gravity, the modified junction conditions for these models impose that the dust particles on the star surface follow geodesic trajectories on the corresponding black hole background. Generically, in these models the star collapses until it reaches a minimum size (and a maximum density) inside the inner horizon of the black hole it creates. Then, it bounces back and reappears through a white hole in a different universe, where it eventually reaches its original size and restarts the process. Along the way, we study Friedmann-Lemaître-Robertson-Walker (FLRW) cosmologies in the same theories that regularize black hole singularities. We find that the cosmological evolution is completely smooth, with the big bang and big crunch singularities predicted by Einstein gravity replaced by cosmological bounces.
Physics Subject Headings (PhySH)
Article Text
References (137)
- J. R. Oppenheimer and H. Snyder, On continued gravitational contraction, Phys. Rev. 56, 455 (1939).
- R. Penrose, Gravitational collapse and space-time singularities, Phys. Rev. Lett. 14, 57 (1965).
- R. Penrose, Gravitational collapse: The role of general relativity, Riv. Nuovo Cimento 1, 252 (1969).
- P. Hajicek and C. Kiefer, Singularity avoidance by collapsing shells in quantum gravity, Int. J. Mod. Phys. D 10, 775 (2001).
- S. D. Mathur, The Fuzzball proposal for black holes: An elementary review, Fortschr. Phys. 53, 793 (2005).
- H. M. Haggard and C. Rovelli, Quantum-gravity effects outside the horizon spark black to white hole tunneling, Phys. Rev. D 92, 104020 (2015).
- V. Husain, J. G. Kelly, R. Santacruz, and E. Wilson-Ewing, Quantum gravity of dust collapse: Shock waves from black holes, Phys. Rev. Lett. 128, 121301 (2022).
- M. Han, C. Rovelli, and F. Soltani, Geometry of the black-to-white hole transition within a single asymptotic region, Phys. Rev. D 107, 064011 (2023).
- G. ’t Hooft and M. J. G. Veltman, One loop divergencies in the theory of gravitation, Ann. Inst. H. Poincaré A 20, 69 (1974).
- M. H. Goroff and A. Sagnotti, The ultraviolet behavior of Einstein gravity, Nucl. Phys. B266, 709 (1986).
- B. Zwiebach, Curvature squared terms and string theories, Phys. Lett. B 156, 315 (1985).
- D. J. Gross and J. H. Sloan, The quartic effective action for the heterotic string, Nucl. Phys. B291, 41 (1987).
- M. T. Grisaru and D. Zanon, model superstring corrections to the Einstein-Hilbert action, Phys. Lett. B 177, 347 (1986).
- A. D. Sakharov, Vacuum quantum fluctuations in curved space and the theory of gravitation, Dokl. Akad. Nauk SSSR 177, 70 (1967).
- M. Visser, Sakharov’s induced gravity: A modern perspective, Mod. Phys. Lett. A 17, 977 (2002).
- S. Endlich, V. Gorbenko, J. Huang, and L. Senatore, An effective formalism for testing extensions to general relativity with gravitational waves, J. High Energy Phys. 09 (2017) 122.
- A. Eichhorn, Asymptotically safe gravity, in Proceeding of the 57th International School of Subnuclear Physics: In Search for the Unexpected (ISSP, 2019).
- J. N. Borissova and B. Dittrich, Towards effective actions for the continuum limit of spin foams, Classical Quantum Gravity 40, 105006 (2023).
- P. Bueno, P. A. Cano, and R. A. Hennigar, Regular black holes from pure gravity, Phys. Lett. B 861, 139260 (2025).
- J. Oliva and S. Ray, A new cubic theory of gravity in five dimensions: Black hole, Birkhoff’s theorem and C-function, Classical Quantum Gravity 27, 225002 (2010).
- R. C. Myers and B. Robinson, Black holes in quasi-topological gravity, J. High Energy Phys. 08 (2010) 067.
- M. H. Dehghani, A. Bazrafshan, R. B. Mann, M. R. Mehdizadeh, M. Ghanaatian, and M. H. Vahidinia, Black holes in quartic quasitopological gravity, Phys. Rev. D 85, 104009 (2012).
- J. Ahmed, R. A. Hennigar, R. B. Mann, and M. Mir, Quintessential Quartic quasi-topological quartet, J. High Energy Phys. 05 (2017) 134.
- A. Cisterna, L. Guajardo, M. Hassaine, and J. Oliva, Quintic quasi-topological gravity, J. High Energy Phys. 04 (2017) 066.
- P. Bueno, P. A. Cano, and R. A. Hennigar, (Generalized) quasi-topological gravities at all orders, Classical Quantum Gravity 37, 015002 (2020).
- P. Bueno, P. A. Cano, R. A. Hennigar, M. Lu, and J. Moreno, Generalized quasi-topological gravities: The whole shebang, Classical Quantum Gravity 40, 015004 (2023).
- J. Moreno and Á. J. Murcia, Classification of generalized quasitopological gravities, Phys. Rev. D 108, 044016 (2023).
- P. Bueno, P. A. Cano, J. Moreno, and Á. Murcia, All higher-curvature gravities as Generalized quasi-topological gravities, J. High Energy Phys. 11 (2019) 062.
- P. A. Cano and Á. Murcia, Electromagnetic quasitopological gravities, J. High Energy Phys. 10 (2020) 125.
- P. A. Cano and Á. Murcia, Resolution of Reissner-Nordström singularities by higher-derivative corrections, Classical Quantum Gravity 38, 075014 (2021).
- P. Bueno, P. A. Cano, J. Moreno, and G. van der Velde, Regular black holes in three dimensions, Phys. Rev. D 104, L021501 (2021).
- P. Bueno, O. Lasso Andino, J. Moreno, and G. van der Velde, On regular charged black holes in three dimensions, arXiv:2503.02930.
- G. Arciniega, P. Bueno, P. A. Cano, J. D. Edelstein, R. A. Hennigar, and L. G. Jaime, Geometric inflation, Phys. Lett. B 802, 135242 (2020).
- P. Wang, H. Wu, H. Yang, and S. Ying, Non-singular string cosmology via corrections, J. High Energy Phys. 10 (2019) 263.
- P. G. S. Fernandes, Singularity resolution and inflation from an infinite tower of regularized curvature corrections, arXiv:2504.07692.
- P. G. S. Fernandes, Regular BTZ black holes from an infinite tower of corrections, arXiv:2504.08565.
- A. D. Sakharov, Nachal’naia stadija rasshirenija Vselennoj i vozniknovenije neodnorodnosti raspredelenija veshchestva, Sov. Phys. JETP 22, 241 (1966).
- J. Bardeen, Non-singular general relativistic gravitational collapse, in Proceedings of the 5th International Conference on Gravitation and the Theory of Relativity (Proceedings of of International Conference GR5, Tbilisi, USSR, 1968), p. 87.
- E. Poisson and W. Israel, Structure of the black hole nucleus, Classical Quantum Gravity 5, L201 (1988).
- I. Dymnikova, Vacuum nonsingular black hole, Gen. Relativ. Gravit. 24, 235 (1992).
- S. A. Hayward, Formation and evaporation of regular black holes, Phys. Rev. Lett. 96, 031103 (2006).
- V. P. Frolov, Information loss problem and a “black hole” model with a closed apparent horizon, J. High Energy Phys. 05 (2014) 049.
- R. Carballo-Rubio, F. Di Filippo, S. Liberati, C. Pacilio, and M. Visser, On the viability of regular black holes, J. High Energy Phys. 07 (2018) 023.
- R. Carballo-Rubio, F. Di Filippo, S. Liberati, and M. Visser, Phenomenological aspects of black holes beyond general relativity, Phys. Rev. D 98, 124009 (2018).
- R. Carballo-Rubio, F. Di Filippo, S. Liberati, and M. Visser, Opening the Pandora’s box at the core of black holes, Classical Quantum Gravity 37, 14 (2020).
- R. Carballo-Rubio, F. Di Filippo, S. Liberati, and M. Visser, Geodesically complete black holes, Phys. Rev. D 101, 084047 (2020).
- E. Franzin, S. Liberati, J. Mazza, and V. Vellucci, Stable rotating regular black holes, Phys. Rev. D 106, 104060 (2022).
- R. Ghosh, M. Rahman, and A. K. Mishra, Regularized stable Kerr black hole: Cosmic censorships, shadow and quasi-normal modes, Eur. Phys. J. C 83, 91 (2023).
- S. Vagnozzi et al., Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A, Classical Quantum Gravity 40, 165007 (2023).
- D. Pedrotti and S. Vagnozzi, Quasinormal modes-shadow correspondence for rotating regular black holes, Phys. Rev. D 110, 084075 (2024).
- M. Calzà, D. Pedrotti, and S. 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).
- M. Calzà, D. Pedrotti, and S. Vagnozzi, Primordial regular black holes as all the dark matter. I. Time-radial-symmetric metrics, Phys. Rev. D 111, 024009 (2025).
- P. C. W. Davies, D. A. Easson, and P. B. Levin, Nonsingular black holes as dark matter, Phys. Rev. D 111, 103512 (2025).
- J. Borissova, S. Liberati, and M. Visser, Violations of the null convergence condition in kinematical transitions between singular and regular black holes, horizonless compact objects, and bounces, Phys. Rev. D 111, 104054 (2025).
- C. Coviello, L. Lehner, and V. Vellucci, Tidal response of regular black holes, Phys. Rev. D 111, 104073 (2025).
- R. Carballo-Rubio et al., Towards a non-singular paradigm of black hole physics, J. Cosmol. Astropart. Phys. 05 (2025) 003.
- V. P. Frolov, M. A. Markov, and V. F. Mukhanov, Through a black hole into a new Universe?, Phys. Lett. B 216, 272 (1989).
- C. Barrabes and V. P. Frolov, How many new worlds are inside a black hole?, Phys. Rev. D 53, 3215 (1996).
- D. A. Easson, Hawking radiation of nonsingular black holes in two-dimensions, J. High Energy Phys. 02 (2003) 037.
- P. Nicolini, A. Smailagic, and E. Spallucci, Noncommutative geometry inspired Schwarzschild black hole, Phys. Lett. B 632, 547 (2006).
- G. J. Olmo and D. Rubiera-Garcia, Reissner-Nordström black holes in extended Palatini theories, Phys. Rev. D 86, 044014 (2012).
- A. B. Balakin, J. P. S. Lemos, and A. E. Zayats, Regular nonminimal magnetic black holes in spacetimes with a cosmological constant, Phys. Rev. D 93, 024008 (2016).
- D. Bazeia, L. Losano, G. J. Olmo, D. Rubiera-Garcia, and A. Sanchez-Puente, Classical resolution of black hole singularities in arbitrary dimension, Phys. Rev. D 92, 044018 (2015).
- A. H. Chamseddine and V. Mukhanov, Nonsingular black hole, Eur. Phys. J. C 77, 183 (2017).
- C. Bambi, D. Rubiera-Garcia, and Y. Wang, Black hole solutions in functional extensions of Born-Infeld gravity, Phys. Rev. D 94, 064002 (2016).
- D. A. Easson, Nonsingular Schwarzschild–de Sitter black hole, Classical Quantum Gravity 35, 235005 (2018).
- C. Bejarano, G. J. Olmo, and D. Rubiera-Garcia, What is a singular black hole beyond general relativity?, Phys. Rev. D 95, 064043 (2017).
- A. Colléaux, S. Chinaglia, and S. Zerbini, Nonpolynomial Lagrangian approach to regular black holes, Int. J. Mod. Phys. D 27, 1830002 (2018).
- P. A. Cano, S. Chimento, T. Ortín, and A. Ruipérez, Regular stringy black holes?, Phys. Rev. D 99, 046014 (2019).
- A. Colleaux, Regular black hole and cosmological spacetimes in non-polynomial gravity theories, Ph.D. thesis, Trento University, 2019.
- M. Guerrero and D. Rubiera-Garcia, Nonsingular black holes in nonlinear gravity coupled to Euler-Heisenberg electrodynamics, Phys. Rev. D 102, 024005 (2020).
- R. Brandenberger, L. Heisenberg, and J. Robnik, Through a black hole into a new Universe, Int. J. Mod. Phys. D 30, 2142001 (2021).
- G. J. Olmo and D. Rubiera-Garcia, Regular black holes in Palatini gravity, arXiv:2209.05061.
- A. Biasi, O. Evnin, and S. Sypsas, de Sitter bubbles from Anti–de Sitter fluctuations, Phys. Rev. Lett. 129, 251104 (2022).
- J. T. S. S. Junior, F. S. N. Lobo, and M. E. Rodrigues, Black holes and regular black holes in coincident gravity coupled to nonlinear electrodynamics, Eur. Phys. J. C 84, 332 (2024).
- J. Ovalle, Schwarzschild black hole revisited: Before the complete collapse, Phys. Rev. D 109, 104032 (2024).
- G. Alencar, K. A. Bronnikov, M. E. Rodrigues, D. Sáez-Chillón Gómez, and M. V. de S. Silva, On black bounce space-times in non-linear electrodynamics, Eur. Phys. J. C 84, 745 (2024).
- K. A. Bronnikov, Regular black holes as an alternative to black bounce, Phys. Rev. D 110, 024021 (2024).
- S. V. Bolokhov, K. A. Bronnikov, and M. V. Skvortsova, A regular center instead of a black bounce, Gravitation Cosmol. 30, 265 (2024).
- M. Skvortsova, Ringing of extreme regular black holes, Gravitation Cosmol. 30, 279 (2024).
- E. Ayon-Beato and A. Garcia, Regular black hole in general relativity coupled to nonlinear electrodynamics, Phys. Rev. Lett. 80, 5056 (1998).
- K. A. Bronnikov, Regular magnetic black holes and monopoles from nonlinear electrodynamics, Phys. Rev. D 63, 044005 (2001).
- E. Ayon-Beato and A. Garcia, The Bardeen model as a nonlinear magnetic monopole, Phys. Lett. B 493, 149 (2000).
- K. A. Bronnikov, Comment on “Regular black hole in general relativity coupled to nonlinear electrodynamics”, Phys. Rev. Lett. 85, 4641 (2000).
- E. Ayon-Beato and A. Garcia, Four parametric regular black hole solution, Gen. Relativ. Gravit. 37, 635 (2005).
- I. Dymnikova, Regular electrically charged structures in nonlinear electrodynamics coupled to general relativity, Classical Quantum Gravity 21, 4417 (2004).
- W. Berej, J. Matyjasek, D. Tryniecki, and M. Woronowicz, Regular black holes in quadratic gravity, Gen. Relativ. Gravit. 38, 885 (2006).
- L. Balart and E. C. Vagenas, Regular black hole metrics and the weak energy condition, Phys. Lett. B 730, 14 (2014).
- Z.-Y. Fan, Critical phenomena of regular black holes in Anti-de Sitter space-time, Eur. Phys. J. C 77, 266 (2017).
- K. A. Bronnikov, Nonlinear electrodynamics, regular black holes and wormholes, Int. J. Mod. Phys. D 27, 1841005 (2018).
- F. Shojai, A. Sadeghi, and R. Hassannejad, Generalized Oppenheimer–Snyder gravitational collapse into regular black holes, Classical Quantum Gravity 39, 085003 (2022).
- J. T. S. S. Junior, F. S. N. Lobo, and M. E. Rodrigues, (Regular) black holes in conformal killing gravity coupled to nonlinear electrodynamics and scalar fields, Classical Quantum Gravity 41, 055012 (2024).
- S. Murk and I. Soranidis, Light rings and causality for nonsingular ultracompact objects sourced by nonlinear electrodynamics, Phys. Rev. D 110, 044064 (2024).
- Z.-C. Li and H. Lü, Regular electric black holes from Einstein-Maxwell-scalar gravity, Phys. Rev. D 110, 104046 (2024).
- X.-Y. Zhang, L. Zhao, and Y.-Q. Wang, Bardeen-Dirac stars in Anti-de Sitter spacetime, J. Cosmol. Astropart. Phys. 01 (2025) 117.
- C. Erices, L. Guajardo, and K. Lara, Reverse stealth construction and its thermodynamic imprints, J. Cosmol. Astropart. Phys. 03 (2025) 051.
- M. Estrada and R. Aros, Pure Lovelock gravity regular black holes, J. Cosmol. Astropart. Phys. 01 (2025) 032.
- H. Huang and X.-P. Rao, Regular black holes and their singular families, Phys. Rev. D 111, 104040 (2025).
- M. Calzá, M. Rinaldi, and S. Zerbini, Topological regular black holes without Cauchy horizon, Phys. Rev. D 112, 024024 (2025).
- R. A. Konoplya and A. Zhidenko, Infinite tower of higher-curvature corrections: Quasinormal modes and late-time behavior of D-dimensional regular black holes, Phys. Rev. D 109, 104005 (2024).
- F. Di Filippo, I. Kolář, and D. Kubiznak, Inner-extremal regular black holes from pure gravity, Phys. Rev. D 111, L041505 (2025).
- R. A. Konoplya and A. Zhidenko, Dymnikova black hole from an infinite tower of higher-curvature corrections, Phys. Lett. B 856, 138945 (2024).
- T.-X. Ma and Y.-Q. Wang, Frozen boson stars in an infinite tower of higher-derivative gravity, Eur. Phys. J. C 85, 542 (2025).
- V. P. Frolov, A. Koek, J. P. Soto, and A. Zelnikov, Regular black holes inspired by quasitopological gravity, Phys. Rev. D 111, 044034 (2025).
- S.-W. Wang, S.-P. Wu, and S.-W. Wei, Are regular black holes from pure gravity classified within the same thermodynamical topology?, Phys. Lett. B 864, 139402 (2025).
- P. Bueno, P. A. Cano, R. A. Hennigar, and A. J. Murcia, Dynamical formation of regular black holes, Phys. Rev. Lett. 134, 181401 (2025).
- P. Bueno, P. A. Cano, R. A. Hennigar, and A. J. Murcia, Regular black holes from thin-shell collapse, Phys. Rev. D 111, 104009 (2025).
- P. S. Joshi, ed., Gravitational Collapse and Spacetime Singularities, Cambridge Monographs on Mathematical Physics (Cambridge University Press, Cambridge, England, 2012).
- A. Ilha and J. P. S. Lemos, Dimensionally continued Oppenheimer-Snyder gravitational collapse. 1. Solutions in even dimensions, Phys. Rev. D 55, 1788 (1997).
- T. Padmanabhan, Some aspects of field equations in generalised theories of gravity, Phys. Rev. D 84, 124041 (2011).
- D. Lovelock, Divergence-free tensorial concomitants, Aequ. Math. 4, 127 (1970).
- D. Lovelock, The Einstein tensor and its generalizations, J. Math. Phys. (N.Y.) 12, 498 (1971).
- T. Padmanabhan and D. Kothawala, Lanczos-Lovelock models of gravity, Phys. Rep. 531, 115 (2013).
- G. W. Horndeski, Second-order scalar-tensor field equations in a four-dimensional space, Int. J. Theor. Phys. 10, 363 (1974).
- W. Israel, Singular hypersurfaces and thin shells in general relativity, Nuovo Cimento B (1965-1970) 44, 1 (1966); 48, 463(E) (1967).
- A. Padilla and V. Sivanesan, Boundary terms and junction conditions for generalized scalar-tensor theories, J. High Energy Phys. 08 (2012) 122.
- R. L. Arnowitt, S. Deser, and C. W. Misner, Canonical variables for general relativity, Phys. Rev. 117, 1595 (1960).
- R. L. Arnowitt, S. Deser, and C. W. Misner, Coordinate invariance and energy expressions in general relativity, Phys. Rev. 122, 997 (1961).
- S. Deser and B. Tekin, Energy in generic higher curvature gravity theories, Phys. Rev. D 67, 084009 (2003).
- J. Moreno and Á. J. Murcia, Cosmological higher-curvature gravities, Classical Quantum Gravity 41, 135017 (2024).
- J. Smoller and B. Temple, Shock-wave solutions of the Einstein equations: The Oppenheimer-Snyder model of gravitational collapse extended to the case of non-zero pressure, Arch. Ration. Mech. Anal. 128, 249 (1994).
- E. Poisson, A Relativist’s Toolkit: The Mathematics of Black-Hole Mechanics (Cambridge University Press, Cambridge, England, 2009).
- D. G. Boulware and S. Deser, String generated gravity models, Phys. Rev. Lett. 55, 2656 (1985).
- J. T. Wheeler, Symmetric solutions to the Gauss-Bonnet extended Einstein equations, Nucl. Phys. B268, 737 (1986).
- G. Lemaitre, The expanding Universe, Mon. Not. R. Astron. Soc. 91, 490 (1931).
- R. C. Tolman, Effect of imhomogeneity on cosmological models, Proc. Natl. Acad. Sci. U.S.A. 20, 169 (1934).
- H. Bondi, Spherically symmetrical models in general relativity, Mon. Not. R. Astron. Soc. 107, 410 (1947).
- D. Christodoulou, Violation of cosmic censorship in the gravitational collapse of a dust cloud, Commun. Math. Phys. 93, 171 (1984).
- H. A. Buchdahl, General relativistic fluid spheres, Phys. Rev. 116, 1027 (1959).
- P. Bueno, P. A. Cano, R. A. Hennigar, Á. J. Murcia, and A. Vicente-Cano, Buchdahl’s theorem in quasitopological gravity (to be published).
- R. A. Hennigar, D. Kubiznak, S. Murk, and I. Soranidis, Thermodynamics of regular black holes in Anti-de Sitter space (to be published).
- I. Davies and H. S. Reall, Nonperturbative second law of black hole mechanics in effective field theory, Phys. Rev. Lett. 132, 171402 (2024).
- S. Hollands, R. M. Wald, and V. G. Zhang, Entropy of dynamical black holes, Phys. Rev. D 110, 024070 (2024).
- A. C. Wall and Z. Yan, Linearized second law for higher curvature gravity and nonminimally coupled vector fields, Phys. Rev. D 110, 084005 (2024).
- M. W. Choptuik, Universality and scaling in gravitational collapse of a massless scalar field, Phys. Rev. Lett. 70, 9 (1993).
- S. Golod and T. Piran, Choptuik’s critical phenomenon in Einstein-Gauss-Bonnet gravity, Phys. Rev. D 85, 104015 (2012).
- N. Deppe, C. D. Leonard, T. Taves, G. Kunstatter, and R. B. Mann, Critical collapse in Einstein-Gauss-Bonnet gravity in five and six dimensions, Phys. Rev. D 86, 104011 (2012).