Abstract
Repulsive gravity is a well known characteristic of naked singularities. In this work, we explore light surfaces and find new effects of repulsive gravity. We compare Kerr naked singularities with the corresponding black hole counterparts and find certain structures that are identified as horizon remnants. We argue that these features might be significant for the comprehension of processes that lead to the formation or eventually destruction of black hole Killing horizons. These features can be detected by observing photon orbits, particularly close to the rotation axis, which can be used to distinguish naked singularities from black holes.
Notes
An interesting speculative interpretation of the super-spinner solutions explores the duality between elementary particles and BHs, with quantum BH as the link between microphysics and macrophysics [37,38,39,40,41]. In any case, the NSs, which are present in the Kerr, Reissner-Nörstrom, and Kerr-Newman spacetimes, provide a perspective of crucial interest regarding the elementary particles description in general relativity and the definition of the characteristic charge, mass, and spin-mass ratio, radius and particles number of self-gravitating objects[42,43,44,45,46,47,48]. In self-gravitating objects such as boson stars or fermion stars, the repulsive gravity factors may -n of a critical charge and particle number of the object itself [49,50,51,52,53,54].
The BH formation after collapse has been associated with trapped surfaces formation, that is, a singularity without trapped surfaces is usually considered as a proof of its naked singularity nature[64,65,66,67,68,69]. Nevertheless, the non-existence of trapped surfaces after or during the gravitational collapse is not a proof of the existence of a NS. It is possible to choose a very particular slicing of spacetime during the formation of a spherically symmetric black hole where no trapped surfaces exist (see also [70, 71]).
Equation \(\varDelta \omega _{\pm }=\mathbf {c}\) can be solved for the spins \(a_z^{\pm }\equiv \sqrt{\left[ {r^2 \left[ 2-\mathbf {c}^2 r (r+2)\right] \pm 2 \sqrt{r^3 \left[ r-4 \mathbf {c}^2 (r+2)\right] }}\right] / {\mathbf {c}^2 (r+2)^2}}\), where \(a_z^-=a_z^+=0\) for \(\mathbf {c}= \pm {2 \sqrt{r-2}}/{r^{3/2}}\). Furthermore, it is clear that the values of \(\mathbf {c}\) such that \(a_z^{\pm }=0\), which correspond to the Schwarzschild case, have as extreme case \(r=3M\). That is, \(a_z\) are curves with equal difference in frequency, which is null, as expected, on the horizon in the extended plane- Fig. (2).
References
Pugliese, D., Quevedo, H.: Eur. Phys. J. C 81 3 258 (2021)
Pugliese, D., Quevedo, H.: Eur. Phys. J. C 78 1 69 (2018)
Pugliese, D., Quevedo, H.: Eur. Phys. J. C 79 3 209 (2019)
Pugliese, D., Quevedo, H.: arXiv:1910.02808 [gr-qc] (2019)
Pugliese, D., Quevedo, H.: arXiv:1910.04996 [gr-qc] (2019)
Pugliese, D., Montani, G.: Entropy 22, 402 (2020)
Pugliese, D., Stuchlik, Z.: Class. Quant. Grav. (2021). https://doi.org/10.1088/1361-6382/abff97
Manko, V.S., Ruiz, E.: Phys. Lett. B 791, 26–29 (2019)
The Event Horizon Telescope Collaboration et al., ApJL 875 (2019) L1
de Felice, F.: Mont. Notice R. astr. Soc 252, 197–202 (1991)
de Felice, F., Usseglio-Tomasset, S.: Class. Quant. Grav. 8, 1871–1880 (1991)
de Felice, F., Usseglio-Tomasset, S.: Gen.Rel.Grav. 24, 10 (1992)
de Felice, F., Yunqiang, Y.: Class. Quant. Grav. 10, 353–364 (1993)
de Felice, F., Di, L., Sigalotti, G.: Ap. J. 389, 386–391 (1992)
Chakraborty, C., Patil, M., et al.: Phys. Rev. D 95(8), 084024 (2017)
Tanatarov, I. V., Zaslavskii, O. B.: Gen.Rel.Grav. 49 9 119 (2017)
Mukherjee, S., Nayak, R.K.: Astrophys. Space Sci. 363(8), 163 (2018)
Zaslavskii., O. B: Phys.Rev.D 98 10 104030 (2018)
Zaslavskii, O.B.: Phys. Rev. D 100(2), 024050 (2019)
de Felice, F.: A&A 45, 65 (1975)
Batic, D., Chin, D., Nowakowski, M.: Eur. Phys. J. C 71, 1624 (2011)
Luongo, O., Quevedo, H.: Phys. Rev. D 90, 084032 (2014)
Patil, M., Joshi, P.S., Malafarina, D.: Phys. Rev. D 83, 064007 (2011)
Maluf, J.W.: Gen. Rel. Grav. 46, 1734 (2014)
Stuchlik, Z.: Bull. Astron. Inst. Czech 31, 129 (1980)
Gariel, J., Santos, N.O., Silk, J.: Phys. Rev. D 90, 063505 (2014)
Pelavas, N., Neary, N., Lake, K.: Class. Quant. Grav. 18, 1319 (2001)
Herdeiro, C., Radu, E.: Phys. Rev. D 89(1240), 18 (2014)
Stuchlik, Z., Pugliese, D., Schee, J., Kucáková, H.: Eur. Phys. J. C 75(9), 451 (2015)
Frolov, A.V., Frolov, V.P.: Phys. Rev. D 90(12), 124010 (2014)
Paranjape, M. B.: Physics Today, in Commentary&Reviews 24 May (2017)
Goswami, R., Joshi, P.S., Singh, P.: Phys. Rev. Lett. 96, 031302 (2006)
Vaz, C., Witten, L.: Phys. Lett. B 442, 90 (1998)
Iguchi, H., Harada, T., Nakao, K.: Prog. Theor. Phys. 101, 1235 (1999)
Iguchi, H., Nakao, K., Harada, T.: Phys. Rev. D 57, 7262 (1998)
Iguchi, H., Harada, T., Nakao, K.I.: Prog. Theor. Phys. 103, 53 (2000)
Lake, M.J., Carr, B.: JHEP 1511, 105 (2015)
Carr, B.J. arXiv:1703.08655 [gr-qc]
Carr, B.J., Mureika, J., Nicolini, P.: JHEP 1507, 052 (2015)
Carr, B.J.: Springer Proc. Phys. 170, 159 (2016)
Prok, Y., et al.: [CLAS Collaboration]. Phys. Lett. B 672, 12 (2009)
D. Pugliese, H. Quevedo, J. A. Rueda H. and R. Ruffini, Phys.Rev.D 88 (2013) 024053
Ruffini, R., Bonazzola, S.: Phys. Rev. 187, 1767 (1969)
Pugliese, D., Quevedo, H., Ruffini, R.: Phys. Rev. D 83, 104052 (2011)
Pugliese, D., Quevedo, H., Ruffini, R.: Eur. Phys. J. C 77(4), 206 (2017)
Pugliese, D., Quevedo, H., Ruffini, R.: Phys. Rev. D 88, 024042 (2013)
Pugliese, D., Quevedo, H., Ruffini, R.: Phys. Rev. 84, 044030 (2011)
Pugliese, D., Quevedo, H., Ruffini, R.: Phys. Rev. D 83, 024021 (2011)
Carr, B., Mentzer, H., Mureika, J., Nicolini, P.: Eur. Phys. J. C 80, 1166 (2020)
Sivaram, C., Sinha, K.P.: Phys. Rev. D 16, 1975 (1977)
Salam, A., Strathdee, J.A.: Phys. Rev. D 18, 4596 (1978)
Holzhey, C.F.E., Wilczek, F.: Nucl. Phys. B 380, 447 (1992)
Oldershaw, R.L., Cosmol, J.: 6 1361 (2010)
Carr, B.J.: Mod. Phys. Lett. A 28, 1340011 (2013)
Cardoso, V., Pani, P., Cadoni, M., Cavaglia, M.: Phys. Rev. D 77(124), 044 (2008)
Comins, N., Schutz, B.F.: Proc. R. Soc. A 364(1717), 211–226 (1978)
Helou, A., Musco, I., Miller, J.C.: Class. Quant. Grav. 34(13), 135012 (2017)
Penrose, R.: Nuovo Cimento Rivista Serie , 1 (1969)
Shapiro, S.L., Teukolsky, S.A.: Am. Sci. 79(4), 330–343 (1991)
Crisford, T., Santos, J.E.: Phys. Rev. Lett. 118, 181101 (2017)
Loeb, A.: In Search of Naked Singularities Scientific American Observations-Opinion May 3 (2020)
Joshi, P.S.: Sci. Am. 300(2), 36–43 (2009)
Harada, T.: Pramana 63(4), 741–753 (2004)
Penrose, R.: JJApA 20, 233 (1999)
Joshi, P.S., Dadhich, N., Maartens, R.: Phys. Rev. D 65, 101501 (2002)
Shapiro, S.L., Teukolsky, S.A.: Philosophical Transactions: Physical Sciences and Engineering 340(1658), 365–390 (1992)
Berger, B. K.: Living Reviews in Relativity 5 1 1 (2002)
Bousso, R., Shahbazi-Moghaddam, A., Tomasevic, M.: Phys. Rev. D 100, 126010 (2019)
Ziaie, A.H., Ranjbar, A., Sepangi, H.R.: Class. Quant. Grav. 32, 025010 (2015)
Joshi, P.S.: Gravitational Collapse and Spacetime Singularities. Cambridge Monographs on Mathematical Physics, New York (2007)
Wald, R.M., Iyer, V.: Phys. Rev. D 44, 3719 (1991)
Shapiro, S.L., Teukolsky, S.A.: Phys. Rev. Lett. 66, 994 (1991)
Apostolatos, T.A., Thorne, K.S.: Phys. Rev. D 46, 2435 (1992)
Jacobson, T., Sotiriou, T.P.: Phys. Rev. Lett. 103, 141101 (2009)
Jacobson, T., Sotiriou, T.P.: J. Phys: Conf. Ser. 222, 012041 (2010)
Barausse, E., Cardoso, V., Khanna, G.: Phys. Rev. Lett. 105, 261102 (2010)
Giacomazzo, B., Rezzolla, L., Stergioulas, N.: Phys. Rev. D 84, 024022 (2011)
Wald, R.M.: Class. Quant. Grav. 16, A177 (1999)
Wald, R.M.: Living Rev. Relativ. 4(1), 6 (2001)
Pugliese, D., Quevedo, H.: to be submitted (2021)
Chrusciel, P.T., Lopes Costa, J., Heusler, M.: Living Rev. Rel. 15, 7 (2012)
Li, Z., Bambi, C.: Phys. Rev. D 87, 124022 (2013)
Pugliese, D., Quevedo, H.: Eur. Phys. J. C 75(5), 234 (2015)
Joshi P. S., Dwivedi I. H.: Phys. Rev. D 47, 5357 (1993)
Acknowledgements
This work was partially supported by UNAM-DGAPA-PAPIIT, Grant No. 114520, Conacyt-Mexico, Grant No. A1-S-31269, and by the Ministry of Education and Science of Kazakhstan, Grant No. BR05236730 and AP05133630.
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
About this article
Cite this article
Pugliese, D., Quevedo, H. Repulsive gravity effects in horizon formation. Gen Relativ Gravit 53, 89 (2021). https://doi.org/10.1007/s10714-021-02858-4
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10714-021-02858-4