Abstract
We illustrate that regular black holes and horizonless stars, typically considered as quite distinct families of black hole mimickers, are intimately intertwined. We show that any spherically symmetric regular black hole can be continuously deformed into a horizonless star under the mild conditions of non-negativity of gravitational energy (Misner-Sharp quasi-local mass), and an assumed linear relation between the latter and the Arnowitt-Deser-Misner (ADM) mass. We illustrate this general result by considering the family of geometries proposed by Hayward as the description of regular black holes, and we also describe the properties of the corresponding horizonless stars. The form of the associated effective stress-energy tensor shows that these horizonless stars can be identified as anisotropic gravastars with a soft surface and inner/outer light rings. We also construct dynamical geometries that could describe the evolution of regular black holes towards horizonless stars, and show that it is plausible that the effective stress-energy tensor in the first stages of evolution is generated by semiclassical effects, in agreement with independent works analyzing semiclassical backreaction.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R. Penrose, Gravitational collapse and space-time singularities, Phys. Rev. Lett. 14 (1965) 57 [INSPIRE].
S.W. Hawking and R. Penrose, The Singularities of gravitational collapse and cosmology, Proc. Roy. Soc. Lond. A 314 (1970) 529 [INSPIRE].
J.M.M. Senovilla and D. Garfinkle, The 1965 Penrose singularity theorem, Class. Quant. Grav. 32 (2015) 124008 [arXiv:1410.5226] [INSPIRE].
R. Carballo-Rubio, F. Di Filippo, S. Liberati and M. Visser, Geodesically complete black holes, Phys. Rev. D 101 (2020) 084047 [arXiv:1911.11200] [INSPIRE].
R. Carballo-Rubio, F. Di Filippo, S. Liberati and M. Visser, Opening the Pandora’s box at the core of black holes, Class. Quant. Grav. 37 (2020) 14 [arXiv:1908.03261] [INSPIRE].
M. Bojowald, Singularities and Quantum Gravity, AIP Conf. Proc. 910 (2007) 294 [gr-qc/0702144] [INSPIRE].
LIGO Scientific and Virgo collaborations, Observation of Gravitational Waves from a Binary Black Hole Merger, Phys. Rev. Lett. 116 (2016) 061102 [arXiv:1602.03837] [INSPIRE].
LIGO Scientific and VIRGO collaborations, GW170104: Observation of a 50-Solar-Mass Binary Black Hole Coalescence at Redshift 0.2, Phys. Rev. Lett. 118 (2017) 221101 [Erratum ibid. 121 (2018) 129901] [arXiv:1706.01812] [INSPIRE].
LIGO Scientific and Virgo collaborations, GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral, Phys. Rev. Lett. 119 (2017) 161101 [arXiv:1710.05832] [INSPIRE].
LIGO Scientific and Virgo collaborations, Tests of General Relativity with the Binary Black Hole Signals from the LIGO-Virgo Catalog GWTC-1, Phys. Rev. D 100 (2019) 104036 [arXiv:1903.04467] [INSPIRE].
LIGO Scientific et al. collaborations, A Gravitational-wave Measurement of the Hubble Constant Following the Second Observing Run of Advanced LIGO and Virgo, Astrophys. J. 909 (2021) 218 [arXiv:1908.06060] [INSPIRE].
LIGO Scientific and Virgo collaborations, Tests of general relativity with binary black holes from the second LIGO-Virgo gravitational-wave transient catalog, Phys. Rev. D 103 (2021) 122002 [arXiv:2010.14529] [INSPIRE].
LIGO Scientific et al. collaborations, Constraints on Cosmic Strings Using Data from the Third Advanced LIGO-Virgo Observing Run, Phys. Rev. Lett. 126 (2021) 241102 [arXiv:2101.12248] [INSPIRE].
LIGO Scientific et al. collaborations, Tests of General Relativity with GWTC-3, arXiv:2112.06861 [INSPIRE].
Event Horizon Telescope collaboration, First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole, Astrophys. J. Lett. 875 (2019) L1 [arXiv:1906.11238] [INSPIRE].
Event Horizon Telescope collaboration, First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way, Astrophys. J. Lett. 930 (2022) L12 [INSPIRE].
Event Horizon Telescope collaboration, First Sagittarius A* Event Horizon Telescope Results. II. EHT and Multiwavelength Observations, Data Processing, and Calibration, Astrophys. J. Lett. 930 (2022) L13 [INSPIRE].
Event Horizon Telescope collaboration, First Sagittarius A* Event Horizon Telescope Results. III. Imaging of the Galactic Center Supermassive Black Hole, Astrophys. J. Lett. 930 (2022) L14 [INSPIRE].
Event Horizon Telescope collaboration, First Sagittarius A* Event Horizon Telescope Results. IV. Variability, Morphology, and Black Hole Mass, Astrophys. J. Lett. 930 (2022) L15 [INSPIRE].
Event Horizon Telescope collaboration, First Sagittarius A* Event Horizon Telescope Results. V. Testing Astrophysical Models of the Galactic Center Black Hole, Astrophys. J. Lett. 930 (2022) L16 [INSPIRE].
Event Horizon Telescope collaboration, First Sagittarius A* Event Horizon Telescope Results. VI. Testing the Black Hole Metric, Astrophys. J. Lett. 930 (2022) L17 [INSPIRE].
J.M. Bardeen, Non-singular general-relativistic gravitational collapse, in the proceedings of the Abstracts of the International Conference GR5, Tbilisi USSR, September 9-13 (1968), p. 174.
A. Borde, Open and closed universes, initial singularities and inflation, Phys. Rev. D 50 (1994) 3692 [gr-qc/9403049] [INSPIRE].
I. Dymnikova, Vacuum nonsingular black hole, Gen. Rel. Grav. 24 (1992) 235 [INSPIRE].
I. Dymnikova, Cosmological term as a source of mass, Class. Quant. Grav. 19 (2002) 725 [gr-qc/0112052] [INSPIRE].
I. Dymnikova, Spherically symmetric space-time with the regular de Sitter center, Int. J. Mod. Phys. D 12 (2003) 1015 [gr-qc/0304110] [INSPIRE].
S.A. Hayward, Formation and evaporation of regular black holes, Phys. Rev. Lett. 96 (2006) 031103 [gr-qc/0506126] [INSPIRE].
V.P. Frolov, Notes on nonsingular models of black holes, Phys. Rev. D 94 (2016) 104056 [arXiv:1609.01758] [INSPIRE].
R. Carballo-Rubio et al., On the viability of regular black holes, JHEP 07 (2018) 023 [arXiv:1805.02675] [INSPIRE].
R. Carballo-Rubio et al., Inner horizon instability and the unstable cores of regular black holes, JHEP 05 (2021) 132 [arXiv:2101.05006] [INSPIRE].
R. Carballo-Rubio et al., Regular black holes without mass inflation instability, JHEP 09 (2022) 118 [arXiv:2205.13556] [INSPIRE].
E. Franzin, S. Liberati, J. Mazza and V. Vellucci, Stable rotating regular black holes, Phys. Rev. D 106 (2022) 104060 [arXiv:2207.08864] [INSPIRE].
G. Chapline, E. Hohlfeld, R.B. Laughlin and D.I. Santiago, Quantum phase transitions and the breakdown of classical general relativity, Int. J. Mod. Phys. A 18 (2003) 3587 [gr-qc/0012094] [INSPIRE].
P.O. Mazur and E. Mottola, Gravitational Condensate Stars: An Alternative to Black Holes, Universe 9 (2023) 88 [gr-qc/0109035] [INSPIRE].
P.O. Mazur and E. Mottola, Gravitational vacuum condensate stars, Proc. Nat. Acad. Sci. 101 (2004) 9545 [gr-qc/0407075] [INSPIRE].
C. Cattoen, T. Faber and M. Visser, Gravastars must have anisotropic pressures, Class. Quant. Grav. 22 (2005) 4189 [gr-qc/0505137] [INSPIRE].
C. Barceló, S. Liberati, S. Sonego and M. Visser, Fate of gravitational collapse in semiclassical gravity, Phys. Rev. D 77 (2008) 044032 [arXiv:0712.1130] [INSPIRE].
C. Barceló, S. Liberati, S. Sonego and M. Visser, Black Stars, Not Holes, Sci. Am. 301 (2009) 38 [INSPIRE].
R. Carballo-Rubio, Stellar equilibrium in semiclassical gravity, Phys. Rev. Lett. 120 (2018) 061102 [arXiv:1706.05379] [INSPIRE].
J. Arrechea, C. Barceló, R. Carballo-Rubio and L.J. Garay, Semiclassical relativistic stars, Sci. Rep. 12 (2022) 15958 [arXiv:2110.15808] [INSPIRE].
M.A. Abramowicz, W. Kluzniak and J.-P. Lasota, No observational proof of the black hole event-horizon, Astron. Astrophys. 396 (2002) L31 [astro-ph/0207270] [INSPIRE].
C.B.M.H. Chirenti and L. Rezzolla, How to tell a gravastar from a black hole, Class. Quant. Grav. 24 (2007) 4191 [arXiv:0706.1513] [INSPIRE].
F.H. Vincent et al., Imaging a boson star at the Galactic center, Class. Quant. Grav. 33 (2016) 105015 [arXiv:1510.04170] [INSPIRE].
V. Cardoso et al., Gravitational-wave signatures of exotic compact objects and of quantum corrections at the horizon scale, Phys. Rev. D 94 (2016) 084031 [arXiv:1608.08637] [INSPIRE].
V. Cardoso et al., Testing strong-field gravity with tidal Love numbers, Phys. Rev. D 95 (2017) 084014 [Addendum ibid. 95 (2017) 089901] [arXiv:1701.01116] [INSPIRE].
V. Cardoso and P. Pani, Tests for the existence of black holes through gravitational wave echoes, Nature Astron. 1 (2017) 586 [arXiv:1709.01525] [INSPIRE].
W. Lu, P. Kumar and R. Narayan, Stellar disruption events support the existence of the black hole event horizon, Mon. Not. Roy. Astron. Soc. 468 (2017) 910 [arXiv:1703.00023] [INSPIRE].
R. Carballo-Rubio, P. Kumar and W. Lu, Seeking observational evidence for the formation of trapping horizons in astrophysical black holes, Phys. Rev. D 97 (2018) 123012 [arXiv:1804.00663] [INSPIRE].
R. Carballo-Rubio, F. Di Filippo, S. Liberati and M. Visser, Phenomenological aspects of black holes beyond general relativity, Phys. Rev. D 98 (2018) 124009 [arXiv:1809.08238] [INSPIRE].
V. Cardoso and P. Pani, Testing the nature of dark compact objects: a status report, Living Rev. Rel. 22 (2019) 4 [arXiv:1904.05363] [INSPIRE].
R. Carballo-Rubio, V. Cardoso and Z. Younsi, Toward very large baseline interferometry observations of black hole structure, Phys. Rev. D 106 (2022) 084038 [arXiv:2208.00704] [INSPIRE].
A. Eichhorn, A. Held and P.-V. Johannsen, Universal signatures of singularity-resolving physics in photon rings of black holes and horizonless objects, JCAP 01 (2023) 043 [arXiv:2204.02429] [INSPIRE].
A. Simpson and M. Visser, Black-bounce to traversable wormhole, JCAP 02 (2019) 042 [arXiv:1812.07114] [INSPIRE].
F.S.N. Lobo et al., Novel black-bounce spacetimes: wormholes, regularity, energy conditions, and causal structure, Phys. Rev. D 103 (2021) 084052 [arXiv:2009.12057] [INSPIRE].
A. Eichhorn, R. Gold and A. Held, Horizonless Spacetimes As Seen by Present and Next-generation Event Horizon Telescope Arrays, Astrophys. J. 950 (2023) 117 [arXiv:2205.14883] [INSPIRE].
A. Eichhorn and A. Held, Quantum gravity lights up spinning black holes, JCAP 01 (2023) 032 [arXiv:2206.11152] [INSPIRE].
E.T. Newman and A.I. Janis, Note on the Kerr spinning particle metric, J. Math. Phys. 6 (1965) 915 [INSPIRE].
M. Azreg-Aïnou, Generating rotating regular black hole solutions without complexification, Phys. Rev. D 90 (2014) 064041 [arXiv:1405.2569] [INSPIRE].
M. Azreg-Aïnou, From static to rotating to conformal static solutions: Rotating imperfect fluid wormholes with(out) electric or magnetic field, Eur. Phys. J. C 74 (2014) 2865 [arXiv:1401.4292] [INSPIRE].
D. Rajan, Complex Spacetimes and the Newman-Janis trick, M.Sc. thesis, School of Mathematics, Statistics and Operations Research, Victoria University of Wellington, Wellington, New Zealand (2015) [arXiv:1601.03862] [INSPIRE].
D. Rajan and M. Visser, Cartesian Kerr-Schild variation on the Newman-Janis trick, Int. J. Mod. Phys. D 26 (2017) 1750167 [arXiv:1601.03532] [INSPIRE].
D.J. Cirilo Lombardo, The Newman-Janis algorithm, rotating solutions and Einstein-Born-Infeld black holes, Class. Quant. Grav. 21 (2004) 1407 [gr-qc/0612063] [INSPIRE].
P. Beltracchi and P. Gondolo, Physical interpretation of Newman-Janis rotating systems. I. A unique family of Kerr-Schild systems, Phys. Rev. D 104 (2021) 124066 [arXiv:2104.02255] [INSPIRE].
P. Beltracchi and P. Gondolo, Physical interpretation of Newman-Janis rotating systems. II. General systems, Phys. Rev. D 104 (2021) 124067 [arXiv:2108.02841] [INSPIRE].
C.W. Misner and D.H. Sharp, Relativistic equations for adiabatic, spherically symmetric gravitational collapse, Phys. Rev. 136 (1964) B571 [INSPIRE].
W.C. Hernandez and C.W. Misner, Observer Time as a Coordinate in Relativistic Spherical Hydrodynamics, Astrophys. J. 143 (1966) 452 [INSPIRE].
S. Hawking, Gravitational radiation in an expanding universe, J. Math. Phys. 9 (1968) 598 [INSPIRE].
S.A. Hayward, Quasilocal gravitational energy, Phys. Rev. D 49 (1994) 831 [gr-qc/9303030] [INSPIRE].
S.A. Hayward, Gravitational energy in spherical symmetry, Phys. Rev. D 53 (1996) 1938 [gr-qc/9408002] [INSPIRE].
M. Visser, Physical observability of horizons, Phys. Rev. D 90 (2014) 127502 [arXiv:1407.7295] [INSPIRE].
A.B. Nielsen and M. Visser, Production and decay of evolving horizons, Class. Quant. Grav. 23 (2006) 4637 [gr-qc/0510083] [INSPIRE].
S.A. Hayward, General laws of black hole dynamics, Phys. Rev. D 49 (1994) 6467 [gr-qc/9303006] [INSPIRE].
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 (2023) 91 [arXiv:2209.12291] [INSPIRE].
F. Di Filippo et al., On the Inner Horizon Instability of Non-Singular Black Holes, Universe 8 (2022) 204 [arXiv:2203.14516] [INSPIRE].
P.V.P. Cunha and C.A.R. Herdeiro, Stationary black holes and light rings, Phys. Rev. Lett. 124 (2020) 181101 [arXiv:2003.06445] [INSPIRE].
P.V.P. Cunha, C. Herdeiro, E. Radu and N. Sanchis-Gual, Exotic Compact Objects and the Fate of the Light-Ring Instability, Phys. Rev. Lett. 130 (2023) 061401 [arXiv:2207.13713] [INSPIRE].
R. Kumar and S.G. Ghosh, Photon ring structure of rotating regular black holes and no-horizon spacetimes, Class. Quant. Grav. 38 (2021) 8 [arXiv:2004.07501] [INSPIRE].
R. Kumar Walia, S.G. Ghosh and S.D. Maharaj, Testing Rotating Regular Metrics with EHT Results of Sgr A*, Astrophys. J. 939 (2022) 77 [arXiv:2207.00078] [INSPIRE].
M. Visser and D.L. Wiltshire, Stable gravastars: An Alternative to black holes?, Class. Quant. Grav. 21 (2004) 1135 [gr-qc/0310107] [INSPIRE].
E. Alesci, S. Bahrami and D. Pranzetti, Asymptotically de Sitter universe inside a Schwarzschild black hole, Phys. Rev. D 102 (2020) 066010 [arXiv:2007.06664] [INSPIRE].
K. Mosani and P.S. Joshi, Regular black hole from regular initial data, arXiv:2306.04298 [INSPIRE].
C. Barceló, V. Boyanov, R. Carballo-Rubio and L.J. Garay, Black hole inner horizon evaporation in semiclassical gravity, Class. Quant. Grav. 38 (2021) 125003 [arXiv:2011.07331] [INSPIRE].
C. Barceló, V. Boyanov, R. Carballo-Rubio and L.J. Garay, Classical mass inflation versus semiclassical inner horizon inflation, Phys. Rev. D 106 (2022) 124006 [arXiv:2203.13539] [INSPIRE].
P. Martin-Moruno and M. Visser, Essential core of the Hawking-Ellis types, Class. Quant. Grav. 35 (2018) 125003 [arXiv:1802.00865] [INSPIRE].
P.V.P. Cunha, E. Berti and C.A.R. Herdeiro, Light-Ring Stability for Ultracompact Objects, Phys. Rev. Lett. 119 (2017) 251102 [arXiv:1708.04211] [INSPIRE].
Acknowledgments
RCR acknowledges financial support through a research grant (29405) from VILLUM fonden. FDF acknowledges financial support by Japan Society for the Promotion of Science Grants-in-Aid for international research fellow No. 21P21318. SL acknowledges funding from the Italian Ministry of Education and Scientific Research (MIUR) under the grant PRIN MIUR 2017-MB8AEZ. CP acknowledges the financial support provided under the European Union’s H2020 ERC, Starting Grant agreement no. DarkGRA-757480 and support under the MIUR PRIN and FARE programmes (GW- NEXT, CUP: B84I20000100001). MV was supported by the Marsden Fund, via a grant administered by the Royal Society of New Zealand.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2211.05817
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Carballo-Rubio, R., Di Filippo, F., Liberati, S. et al. A connection between regular black holes and horizonless ultracompact stars. J. High Energ. Phys. 2023, 46 (2023). https://doi.org/10.1007/JHEP08(2023)046
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2023)046