Abstract
We propose a two-parameter, static and spherically symmetric regular geometry, which, for specific parameter values represents a regular black hole. The matter required to support such spacetimes within the framework of general relativity (GR), is found to violate the energy conditions, though not in the entire domain of the radial coordinate. A particular choice of the parameters reduces the regular black hole to a singular, mutated Reissner–Nordström geometry. It also turns out that our regular black hole is geodesically complete. Fortunately, despite energy condition violation, we are able to construct a viable source, within the framework of GR coupled to matter, for our regular geometry. The source term involves a nonlinear magnetic monopole in a chosen version of nonlinear electrodynamics. We also suggest an alternative approach towards constructing a source, using the effective Einstein equations which arise in the context of braneworld gravity. Finally, we obtain the circular shadow profile of our regular black hole and provide a preliminary estimate of the metric parameters using recent observational results from the EHT collaboration.
Similar content being viewed by others
References
Abbott, B.P., et al.: Phys. Rev. Lett. 116, 061102 (2016). https://doi.org/10.1103/PhysRevLett.116.061102
Abbott, B.P., et al.: Phys. Rev. Lett. 116, 241103 (2016). https://doi.org/10.1103/PhysRevLett.116.241103
Abbott, B.P., et al.: Phys. Rev. Lett. 118, 221101 (2017). https://doi.org/10.1103/PhysRevLett.118.221101
Abbott, B.P., et al.: Phys. Rev. Lett. 119, 161101 (2017). https://doi.org/10.1103/PhysRevLett.119.161101
Akiyama, K., et al.: Astrophys. J. Lett. 875, L1 (2019). https://doi.org/10.3847/2041-8213/ab0ec7
Akiyama, K., et al.: Astrophys. J. Lett. 875, L2 (2019). https://doi.org/10.3847/2041-8213/ab0c96
Akiyama, K., et al.: Astrophys. J. Lett. 875, L3 (2019). https://doi.org/10.3847/2041-8213/ab0c57
Akiyama, K., et al.: Astrophys. J. Lett. 875, L4 (2019). https://doi.org/10.3847/2041-8213/ab0e85
Akiyama, K., et al.: Astrophys. J. Lett. 875, L5 (2019). https://doi.org/10.3847/2041-8213/ab0f43
Akiyama, K., et al.: Astrophys. J. Lett. 875, L6 (2019). https://doi.org/10.3847/2041-8213/ab1141
Akiyama, K., et al.: Astrophys. J. Lett. 930, L12 (2022). https://doi.org/10.3847/2041-8213/ac6674
Akiyama, K., et al.: Astrophys. J. Lett. 930, L13 (2022). https://doi.org/10.3847/2041-8213/ac6675
Akiyama, K., et al.: Astrophys. J. Lett. 930, L14 (2022). https://doi.org/10.3847/2041-8213/ac6429
Akiyama, K., et al.: Astrophys. J. Lett. 930, L15 (2022). https://doi.org/10.3847/2041-8213/ac6736
Akiyama, K., et al.: Astrophys. J. Lett. 930, L16 (2022). https://doi.org/10.3847/2041-8213/ac6672
Akiyama, K., et al.: Astrophys. J. Lett. 930, L17 (2022). https://doi.org/10.3847/2041-8213/ac6756
Hawking, S.W., Ellis, G.F.R.: The Large Scale Structure of Spacetime. Cambridge University Press, Cambridge (1973)
Ansoldi,S.: In: Conference on Black Holes and Naked Singularities, Milano, Italy (2007). arXiv:0802.0330 [gr-qc]
Zaslavskii, O.B.: Phys. Lett. B 688, 278–280 (2010). https://doi.org/10.1016/j.physletb.2010.04.031
Sakharov, A.D.: Zh. Eksp. Teor. Fiz. 49, 345 (1966) [Sov. Phys. JETP 22, 241 (1966)]
Gliner, E.B.: Sov. Phys. JETP 22, 378 (1966)
Bardeen, J.M.: In: Proceedings of International Conference GR5, Tbilisi, USSR, p. 174 (1968
Bardeen, J.M.: arXiv:1406.4098
Bardeen, J.M.: arXiv:1811.06683
Hayward, S.A.: Phys. Rev. Lett. 96, 031103 (2006). https://doi.org/10.1103/PhysRevLett.96.031103
Roman, T.A., Bergmann, P.G.: Phys. Rev. D 28, 1265 (1983). https://doi.org/10.1103/PhysRevD.28.1265
Dymnikova, I.: Gen. Relativ. Gravit. 24, 235 (1992). https://doi.org/10.1007/BF00760226
Dymnikova, I.: Int. J. Mod. Phys. D 12, 1015 (2003). https://doi.org/10.1142/S021827180300358X
Ayon-Beato, E., Garcia, A.: Phys. Rev. Lett. 80, 5056 (1998). https://doi.org/10.1103/PhysRevLett.80.5056
Ayon-Beato, E., Garcia, A.: Phys. Lett. B 464, 25 (1999). https://doi.org/10.1016/S0370-2693/899/901038-2
Frolov, V.P.: Phys. Rev. D 94, 104056 (2016). https://doi.org/10.1103/PhysRevD.94.104056
Frolov, V.P.: J. High Energy Phys. 05, 049 (2014). https://doi.org/10.1007/JHEP05(2014)049
Frolov, V.P., Zelnikov, A.: Phys. Rev. D 95, 124028 (2017). https://doi.org/10.1103/PhysRevD.95.124028
Balart, L., Vagenas, E.C.: Phys. Rev. D 90, 124045 (2014). https://doi.org/10.1103/PhysRevD.90.124045
Bronnikov, K.A.: Phys. Rev. D 63, 044005 (2001). https://doi.org/10.1103/PhysRevD.63.044005
Simpson, A., Visser, M.: J. Cosmol. Astropart. Phys. 02, 042 (2019). https://doi.org/10.1088/1475-7516/2019/02/042
Carballo-Rubio, R., Di Filippo, F., Liberati, S., Pacilio, C., Visser, M.: J. High Energy Phys. 07, 023 (2018). https://doi.org/10.1007/JHEP07(2018)023
Carballo-Rubio, R., Di Filippo, F., Liberati, S., Visser, M.: Phys. Rev. D 98, 124009 (2018). https://doi.org/10.1103/PhysRevD.98.124009
Bambi, C., Modesto, L.: Phys. Lett. B 721, 329 (2013). https://doi.org/10.1016/j.physletb.2013.03.025
Ghosh, S.G., Maharaj, S.D.: Eur. Phys. J. C 75, 7 (2015). https://doi.org/10.1140/epjc/s10052-014-3222-7
Sajadi, S., Riazi, N.: Gen. Relativ. Gravit. 49, 45 (2017). https://doi.org/10.1007/s10714-017-2209-8
Roy, P.D., Kar, S.: Phys. Rev. D 106, 044028 (2022). https://doi.org/10.1103/PhysRevD.106.044028
Pal, K., Pal, K., Roy, P., Sarkar, T.: Eur. Phys. J. C 83, 397 (2023). https://doi.org/10.1140/epjc/s10052-023-11558-z
Ayon-Beato, E., Garcia, A.: Gen. Relativ. Gravit. 31, 629 (1999). https://doi.org/10.1023/A:1026640911319
Ayon-Beato, E., Garcia, A.: Phys. Lett. B 493, 149 (2000). https://doi.org/10.1016/S0370-2693/800/901125-4
Ayon-Beato, E., Garcia, A.: Gen. Relativ. Gravit. 37, 635 (2005). https://doi.org/10.1007/s10714-005-0050-y
Fan, Z.Y.: Eur. Phys. J. C 77, 266 (2017). https://doi.org/10.1140/epjc/s10052-017-4830-9
Bronnikov, K.A.: Phys. Rev. Lett. 85, 4641 (2000). https://doi.org/10.1103/PhysRevLett.85.4641
Bronnikov, K.A.: Int. J. Mod. Phys. D 27, 1841005 (2018). https://doi.org/10.1142/S0218271818410055
Fan, Z.Y., Wang, X.: Phys. Rev. D 94, 124027 (2016). https://doi.org/10.1103/PhysRevD.94.124027
Bokulić, A., Smolić, I., Jurić, T.: Phys. Rev. D 106, 064020 (2022). https://doi.org/10.1103/PhysRevD.106.064020
Poisson, E., Israel, W.: Phys. Rev. Lett. 63, 1663 (1989). https://doi.org/10.1103/PhysRevLett.63.1663
Poisson, E., Israel, W.: Phys. Rev. D 41, 1796 (1990). https://doi.org/10.1103/PhysRevD.41.1796
Bonanno, A., Khosravi, A.-P., Saueressig, F.: Phys. Rev. D 103, 124027 (2021). https://doi.org/10.1103/PhysRevD.103.124027
Carballo-Rubio, R., Di Filippo, F., Liberati, S., Pacilio, C., Visser, M.: J. Cosmol. Astropart. Phys. 09, 118 (2022). https://doi.org/10.1007/JHEP09/82022/9118
Einstein, A., Rosen, N.: Phys. Rev. 48, 73 (1935). https://doi.org/10.1103/PhysRev.48.73
Zakhary, E., Mcintosh, C.B.G.: Gen. Relativ. Gravit. 29, 539 (1997)
Hu, H.W., Lan, C., Miao Lan, Y.G.: arXiv:2303.03931 [gr-qc]
Wald, R.M.: General Relativity. Chicago Univ. Pr, Chicago (1984)
Zhou, T., Modesto, L.: Phys. Rev. D 107, 044016 (2023). https://doi.org/10.1103/PhysRevD.107.044016
Carballo-Rubio, R., Di Filippo, F., Liberati, S., Visser, M.: Phys. Rev. D 101, 084047 (2020). https://doi.org/10.1103/PhysRevD.101.084047
Carballo-Rubio, R., Di Filippo, F., Liberati, S., Visser, M.: J. High Energy Phys. 02, 122 (2022). https://doi.org/10.1007/JHEP02(2022)122
Pal, K., Pal, K., Sarkar, T.: arXiv:2307.09382 (2023)
Torres, R.: arXiv:2208.12713 [gr-qc]
Toshmatov, B., Bambi, C., Ahmedov, B., Abdujabbarov, A., Stuchlik, Z.: Eur. Phys. J. C 77, 542 (2017). https://doi.org/10.1140/epjc/s10052-017-5112-2
Lan, C., Miao, Y.-G., Zang, Y.-X.: Eur. Phys. J. C 82, 231 (2022). https://doi.org/10.1140/epjc/s10052-022-10200-8
Bronnikov, K.A.: Particles 1, 5 (2018). https://doi.org/10.3390/particles1010005
Bronnikov, K.A., Fabris, J.C.: Phys. Rev. Lett. 96, 251101 (2006). https://doi.org/10.1103/PhysRevLett.96.251101
Bronnikov, K.A., Walia, R.K.: Phys. Rev. D 105, 044039 (2022). https://doi.org/10.1103/PhysRevD.105.044039
Maartens, R., Koyama, K.: Living Rev. Relativ. 13, 5 (2010). https://doi.org/10.12942/lrr-2010-5
Bardeen, J.M.: In: DeWitt, C., DeWitt, B.S. (eds.) Black Holes (Les Astres Occlus), (New York: Gordon and Breach), 215 (1973). https://www.google.co.in/books/edition/Black_Holes/sUr-EVqZLckC?hl=en &gbpv=1 &pg=PA215 &printsec=frontcover
Perlick, V., Tsupko, O.Y.: Phys. Rep. 947, 1–39 (2022). https://doi.org/10.1016/j.physrep.2021.10.004
Claudel, C.M., Virbhadra, K.S., Ellis, G.F.R.: J. Math. Phys. 42, 818–838 (2001). https://doi.org/10.1063/1.1308507
Chen, D., Gao, C., Liu, X., Yu, C.: Eur. Phys. J. C 81, 700 (2021). https://doi.org/10.1140/epjc/s10052-021-09510-0
Medeiros, L., et al.: Astrophys. J. Lett. 947, L7 (2023). https://doi.org/10.3847/2041-8213/acc32d
Blakeslee, J.P., et al.: Astrophys. J. Lett. 694, 556–572 (2009). https://doi.org/10.1088/0004-637X/694/1/556
Bird, S., Harris, W.E., Blakeslee, J.P., Flynn, C.: Astron. Astrophys. 524, A71 (2010). https://doi.org/10.1051/0004-6361/201014876
Cantiello, M., et al.: Astrophys. J. Lett. 854, L31 (2018). https://doi.org/10.3847/2041-8213/aaad64
Do, T., et al.: Science 365(6454), 664–668 (2019)
Abuter, R., et al.: Astron. Astrophys. 657, L12 (2022). https://doi.org/10.1051/0004-6361/202142465
Abuter, R., et al.: Astron. Astrophys. 636, L5 (2020). https://doi.org/10.1051/0004-6361/202037813
Dai, De.-C., Stojkovic, D.: Phys. Rev. D 100, 083513 (2019). https://doi.org/10.48550/arXiv.1910.00429
Ghasemi-Nodehi, M., Chakraborty, C., Yu, Q., Lu, Y.: Eur. Phys. J. C 81, 939 (2021). https://doi.org/10.48550/arXiv.2109.14903
Takahashi, R.: Astrophys. J. 611, 996 (2004). https://doi.org/10.48550/arXiv.astro-ph/0405099
Synge, J.L.: Mon. Not. R. Soc. 131, 462 (1966). https://doi.org/10.1093/mnras/131.3.463
Simonetti, J.H., Kavic, M.J., Minic, D., Stojkovic, D., Dai, De.-C.: Phys. Rev. D 104, 081502 (2021). https://doi.org/10.48550/arXiv.2007.12184
Repin, S.V., Bugaev, M.A., Novikov, I.D., Novikov, I.D., Jr.: Astron. Rep. 66(10), 835 (2022)
Bugaev, M.A., Novikov, I.D., Repin, S.V., Samorodskaya, P.S.: arXiv:2305.18041
Newman, E.T., Janis, A.I.: J. Math. Phys. 6, 915 (1965). https://doi.org/10.1063/1.1704350
Acknowledgements
AK expresses gratitude to Poulami Dutta Roy, Soumya Jana and Pritam Banerjee for their valuable inputs during various discussions. He also thanks Indian Institute of Technology Kharagpur, India, for support through a fellowship and for allowing him to use available computational facilities.
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.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Kar, A., Kar, S. Novel regular black holes: geometry, source and shadow. Gen Relativ Gravit 56, 52 (2024). https://doi.org/10.1007/s10714-024-03238-4
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10714-024-03238-4