Abstract
In this manuscript, we study photonsphere, shadow, quasinormal modes, Hawking temperature, and greybody bounds of a non-rotating Simpson–Visser black hole which is a regular black hole. We observe that though the radius of the photonsphere does depend on the Simpson–Visser parameter \(\alpha \), the shadow radius is independent of it. The shadow radius is found to be equal to that for Schwarzschild black hole. We, then, study quasinormal frequencies of the Simpson–Visser black hole for scalar and electromagnetic perturbations with the help of 6th-order WKB method. We tabulate values of quasinormal frequencies for various values of \(\alpha \), angular momentum \(\ell \), and overtone number n. We also graphically show the dependence of real and imaginary parts of quasinormal frequency on \(\alpha \) and \(\ell \). Additionally, We study the convergence of the WKB method for various values of pair \((n,\ell )\). Finally, we shed light on the dependence of the Hawking temperature on the parameter \(\alpha \) and the dependence of greybody bounds on \(\alpha \) and \(\ell \).
Similar content being viewed by others
Data Availability Statement
We do not have any additional data to present.
References
A. Einstein, Lens-like action of a star by the deviation of light in the gravitational field. Science 84, 506–507 (1936)
P. Nicolini, A. Smailagic, E. Spallucci, Noncommutative geometry inspired Schwarzschild black hole. Phys. Lett. B 632, 547–551 (2006). arXiv:gr-qc/0510112
P. Nicolini, Noncommutative black holes, the final appeal to quantum gravity: a review. Int. J. Mod. Phys. A 24, 1229–1308 (2009)
E. Spallucci, A. Smailagic, P. Nicolini, Non-commutative geometry inspired higher-dimensional charged black holes. Phys. Lett. B 670, 449–454 (2009)
P. Nicolini, E. Spallucci, Noncommutative geometry inspired wormholes and dirty black holes. Class. Quant. Grav. 27, 015010 (2010)
A.B. Balakin, A.E. Zayats, Non-minimal Wu-Yang monopole. Phys. Lett. B 644, 294–298 (2007). arXiv:gr-qc/0612019
A.B. Balakin, J.P.S. Lemos, A.E. Zayats, Magnetic black holes and monopoles in a nonminimal Einstein-Yang-Mills theory with a cosmological constant: exact solutions. Phys. Rev. D 93(8), 084004 (2016)
Z. Roupas, Detectable universes inside regular black holes. Eur. Phys. J. C 82(3), 255 (2022)
A. Bonanno, M. Reuter, Renormalization group improved black hole space-times. Phys. Rev. D 62, 043008 (2000)
L. Modesto, Disappearance of black hole singularity in quantum gravity. Phys. Rev. D 70, 124009 (2004). arXiv:gr-qc/0407097
R. Gambini, J. Pullin, Black holes in loop quantum gravity: the complete space-time. Phys. Rev. Lett. 101, 161301 (2008)
B. Koch, F. Saueressig, Black holes within asymptotic safety. Int. J. Mod. Phys. A 29(8), 1430011 (2014)
A. Perez, Black holes in loop quantum gravity. Rept. Prog. Phys. 80(12), 126901 (2017)
N. Bodendorfer, F.M. Mele, J. Münch, Mass and horizon Dirac observables in effective models of quantum black-to-white hole transition. Class. Quant. Grav. 38(9), 095002 (2021). arXiv:1912.00774 [gr-qc]
N. Bodendorfer, F.M. Mele, J. Münch, (b, v)-type variables for black to white hole transitions in effective loop quantum gravity. Phys. Lett. B 819, 136390 (2021). arXiv:1911.12646 [gr-qc]
M. Bojowald, Black-hole models in loop quantum gravity. Universe 6(8), 125 (2020). arXiv:2009.13565 [gr-qc]
S. Brahma, C.-Y. Chen, D.-H. Yeom, Testing loop quantum gravity from observational consequences of nonsingular rotating black holes. Phys. Rev. Lett. 126(18), 181301 (2021). arXiv:2012.08785 [gr-qc]
S. Ansoldi, Spherical black holes with regular center: a review of existing models including a recent realization with Gaussian sources, in Conference on Black Holes and Naked Singularities (2008). Preprint at arXiv:0802.0330 [gr-qc]
J.M. Bardeen, Non-singular general-relativistic gravitational collapse, in Proceedings of GR5 URSS, Tbilisi, 174 (1968)
I. Dymnikova, Vacuum nonsingular black hole. Gen. Relat. Gravit. 24, 235242 (1992)
J.P.S. Lemos, V.T. Zanchin, Regular black holes: electrically charged solutions, Reissner-Nordström outside a de sitter core. Phys. Rev. D 83, 124005 (2011)
A. Kumar, S.G. Ghosh, S.D. Maharaj, Nonsingular black hole chemistry. Phys. Dark Univ. 30, 100634 (2020)
A. Eichhorn, A. Held, Image features of spinning regular black holes based on a locality principle. Eur. Phys. J. C 81, 933 (2021)
K. Akiyama et al., (Event Horizon Telescope), First M87 event horizon telescope results. I. The shadow of the supermassive black hole. Astrophys. J. Lett. 875, L1 (2019)
K. Akiyama et al., (Event Horizon Telescope), 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, L12 (2022)
J.M. Bardeen, W.H. Press, S.A. Teukolsky, Rotating black holes: locally nonrotating frames, energy extraction, and scalar synchrotron radiation. Astrophys. J. 178, 347–370 (1972)
J.L. Synge, The escape of photons from gravitationally intense stars. Mon. Not. R. Astron. Soc. 131, 463–466 (1966)
J.P. Luminet, Image of a spherical black hole with thin accretion disk. Astron. Astrophys. 75, 228–235 (1979)
R. Narayan, M.D. Johnson, C.F. Gammie, The shadow of a spherically accreting black hole. Astrophys. J. 885, L33 (2019)
Y. Guo, Y.-G. Miao, Charged black-bounce spacetimes: photon rings, shadows and observational appearances. Nucl. Phys. B 983, 115938 (2022). arXiv:2112.01747 [gr-qc]
R.C. Pantig, P.K. Yu, E.T. Rodulfo, A. Övgün, Shadow and weak deflection angle of extended uncertainty principle black hole surrounded with dark matter. Ann. Phys. 436, 168722 (2022)
R.A. Konoplya, A. Zhidenko, Solutions of the Einstein equations for a black hole surrounded by a galactic halo. Astrophys. J. 933, 166 (2022)
R.A. Konoplya, Shadow of a black hole surrounded by dark matter. Phys. Lett. B 795, 1–6 (2019). arXiv:1905.00064 [gr-qc]
X. Zhaoyi, X. Hou, X. Gong, J. Wang, Black hole space-time in dark matter halo. JCAP 09, 038 (2018)
X. Zhaoyi, X. Gong, S.-N. Zhang, Black hole immersed dark matter halo. Phys. Rev. D 101, 024029 (2020)
R.C. Pantig, E.T. Rodulfo, Rotating dirty black hole and its shadow. Chin. J. Phys. 68, 236–257 (2020)
W. Javed, H. Irshad, R.C. Pantig, A. Övgün, Weak deflection angle by Kalb-Ramond traversable wormhole in plasma and dark matter mediums. Universe (2022). https://doi.org/10.3390/universe8110599
W. Javed, S. Riaz, R.C. Pantig, A. Övgün, Weak gravitational lensing in dark matter and plasma mediums for wormhole-like static aether solution. Eur. Phys. J. C 82, 1057 (2022)
K. Jusufi, M. Jamil, T. Zhu, Shadows of Sgr \(A^*\) black hole surrounded by superfluid dark matter halo. Eur. Phys. J. C 80, 354 (2020). arXiv:2005.05299 [gr-qc]
S. Nampalliwar, S. Kumar, K. Jusufi, W. Qiang, M. Jamil, P. Salucci, Modeling the Sgr A* Black Hole Immersed in a Dark Matter Spike. Astrophys. J. 916, 116 (2021)
C.V. Vishveshwara, Stability of the Schwarzschild metric. Phys. Rev. D 1, 2870 (1970)
W.H. Press, Long wave trains of gravitational waves from a vibrating black hole. ApJ 170, L105 (1971)
S. Chandrasekhar, S. Detweiler, The quasi-normal modes of the Schwarzschild black hole. Proc. R. Soc. Lond. A 344, 441 (1975)
C. Ma, Y. Gui, W. Wang, F. Wang, Massive scalar field quasinormal modes of a Schwarzschild black hole surrounded by quintessence. Cent. Eur. J. Phys. 6, 194 (2008). [arXiv:gr-qc/0611146]
D.J. Gogoi, U.D. Goswami, A new f(R) gravity model and properties of gravitational waves in it. Eur. Phys. J. C 80, 1101 (2020)
D.J. Gogoi, U.D. Goswami, Gravitational waves in f (R) gravity power law model. Indian J. Phys. 96, 637 (2022)
D. Liang, Y. Gong, S. Hou, Y. Liu, Polarizations of gravitational waves in f(R) gravity. Phys. Rev. D 95, 104034 (2017)
R. Oliveira, D.M. Dantas, C.A.S. Almeida, Quasinormal frequencies for a black hole in a bumblebee gravity. EPL 135, 10003 (2021)
D.J. Gogoi, U.D. Goswami, Quasinormal modes of black holes with non-linear-electrodynamic sources in Rastall gravity. Phys. Dark Univ. 33, 100860 (2021)
J.P.M. Graça, I.P. Lobo, Scalar QNMs for higher dimensional black holes surrounded by quintessence in Rastall gravity. Eur. Phys. J. C 78, 101 (2018)
Y. Zhang, Y.X. Gui, F. Li, Quasinormal modes of a Schwarzschild black hole surrounded by quintessence: electromagnetic perturbations. Gen. Relativ. Gravit. 39, 1003 (2007). [arXiv:gr-qc/0612010]
M. Bouhmadi-L’opez, S. Brahma, C.-Y. Chen, P. Chen, D. Yeom, A consistent model of non-singular Schwarzschild black hole in loop quantum gravity and its quasinormal modes. J. Cosmol. Astropart. Phys. 07, 066 (2020)
J. Liang, Quasinormal modes of the Schwarzschild black hole surrounded by the quintessence field in Rastall gravity. Commun. Theor. Phys. 70(695), 15 (2018)
Y. Hu, C.-Y. Shao, Y.-J. Tan, C.-G. Shao, K. Lin, W.-L. Qian, Scalar quasinormal modes of nonlinear charged black holes in Rastall gravity. EPL 128, 50006 (2020)
S. Giri, H. Nandan, L.K. Joshi, S.D. Maharaj, Geodesic stability and quasinormal modes of non-commutative Schwarzschild black hole employing Lyapunov exponent. Eur. Phys. J. Plus 137, 181 (2022)
D.J. Gogoi, R. Karmakar, U.D. Goswami, Quasinormal modes of non-linearly charged black holes surrounded by a cloud of strings in Rastall gravity (2021). Preprint at arXiv:2111.00854
A. Övgün, İ Sakallı, J. Saavedra, Quasinormal modes of a Schwarzschild Black hole immersed in an electromagnetic universe. Chin. Phys. C 42(10), 105102 (2018)
A. Rincon, P.A. Gonzalez, G. Panotopoulos, J. Saavedra, Y. Vasquez, Quasinormal modes for a non-minimally coupled scalar field in a five-dimensional Einstein-Power- Maxwell background. Eur. Phys. J. Plus 137(11), 1278 (2022)
P.A. González, Á. Rincoń, J. Saavedra, Y. Vásquez, Superradiant instability and charged scalar quasinormal modes for (2+1)- dimensional Coulomb-like AdS black holes from nonlinear electrodynamics. Phys. Rev. D 104(8), 084047 (2021)
G. Panotopoulos, Á. Rincoń, Quasinormal spectra of scale-dependent Schwarzschild-de Sitter black holes. Phys. Dark Univ. 31, 100743 (2021)
R.G. Daghigh, M.D. Green, Validity of the WKB approximation in calculating the asymptotic quasinormal modes of black holes. Phys. Rev. D 85, 127501 (2012). [arXiv:1112.5397 [gr-qc]]
R.G. Daghigh, M.D. Green, Highly real, highly damped, and other asymptotic quasinormal modes of Schwarzschild-Anti De Sitter black holes. Class. Quant. Grav. 26, 125017 (2009)
A. Zhidenko, Quasinormal modes of Schwarzschild de Sitter black holes. Class. Quantum Grav. 21, 273–280 (2004)
A. Zhidenko, Quasi-normal modes of the scalar hairy black hole. Class. Quantum Grav. 23, 3155–3164 (2006)
R.A. Konoplya, A. Zhidenko, Quasinormal modes of black holes: from astrophysics to string theory. Rev. Mod. Phys. 83, 793–836 (2011). [arXiv:1102.4014 [gr-qc]]
Y. Hatsuda, Quasinormal modes of black holes and Borel summation. Phys. Rev. D 101(2), 024008 (2020)
D.S. Eniceicu, M. Reece, Quasinormal modes of charged fields in Reissner-Nordström backgrounds by Borel-Padé summation of Bender-Wu series. Phys. Rev. D 102(4), 044015 (2020)
S. Lepe, J. Saavedra, Quasinormal modes, superradiance and area spectrum for 2+1 acoustic black holes. Phys. Lett. B 617, 174–181 (2005)
M. Chabab, H. El Moumni, S. Iraoui, K. Masmar, Phase transition of charged-AdS black holes and quasinormal modes: a time domain analysis. Astrophys. Space Sci. 362(10), 192 (2017)
M. Chabab, H. El Moumni, S. Iraoui, K. Masmar, Behavior of quasinormal modes and high dimension RN-AdS black hole phase transition. Eur. Phys. J. C 76(12), 676 (2016)
M. Okyay, A. Övgün, Nonlinear electrodynamics effects on the black hole shadow, deflection angle, quasinormal modes and greybody factors. J. Cosmol. Astropart. Phys. 2022, 009 (2022)
A. Övgün, K. Jusufi, Quasinormal modes and greybody factors of f(R) Gravity minimally coupled to a cloud of strings in 2 + 1 dimensions. Ann. Phys. 395, 138 (2018)
R.C. Pantig, L. Mastrototaro, G. Lambiase, A. Övgün, Shadow, lensing, quasinormal modes, greybody bounds and neutrino propagation by dyonic ModMax black holes. Eur. Phys. J. C 82(12), 1155 (2022)
Y. Yang, D. Liu, A. Övgün, Z. W. Long, Z. Xu, Quasinormal modes of Kerr-like black bounce spacetime, [arXiv:2205.07530 [gr-qc]]
Y. Yang, D. Liu, A. Övgün, Z. W. Long, Z. Xu, Probing hairy black holes caused by gravitational decoupling using quasinormal
S.W. Hawking, Commun. Math. Phys. 43, 199 (1975). (Erratum: Commun.Math.Phys. 46, 206 (1976))
H. Hassanabadi, W.S. Chung, B.C. Lütfüoğlu, E. Maghsoodi, Effects of a new extended uncertainty principle on Schwarzschild and Reissner-Nordström black holes thermodynamics. Int. J. Mod. Phys. A 36, 2150036 (2021)
S. Hassanabadi, J. Kříž, W.S. Chung, B.C. Lütfüoğlu, E. Maghsoodi, H. Hassanabadi, Thermodynamics of the Schwarzschild and Reissner-Nordström black holes under higher-order generalized uncertainty principle. Eur. Phys. J. Plus 136, 918 (2021)
H. Chen, B.C. Lütfüoğlu, H. Hassanabadi, Z.-W. Long, Thermodynamics of the Reissner-Nordström black hole with quintessence matter on the EGUP framework. Phys. Lett. B 827, 136994 (2022)
Y.P. Zhang, S.W. Wei, Y.X. Liu, Topological approach to derive the global Hawking temperature of (massive) BTZ black hole. Phys. Lett. B 810, 135788 (2020)
A. Övgün, I. Sakalli, Hawking radiation via gaussbonnet theorem. Ann. Phys. 413, 168071 (2020)
S.I. Kruglov, Magnetically charged black hole in framework of nonlinear electrodynamics model. Int. J. Mod. Phys. A 33, 1850023 (2018)
S. Fernando, Greybody factors of charged dilaton black holes in 2 + 1 dimensions. Gen. Relativ. Gravit. 37, 461481 (2005)
W. Kim, J.J. Oh, Greybody factor and hawking radiation of charged dilatonic black holes. J. Korean Phys. Soc. 52, 986–991 (2008)
J. Escobedo, Greybody factors, Master’s Thesis, Uni. of Amsterdam 6 (2008)
M.K. Parikh, W. Frank, Hawking radiation as tunneling. Phys. Rev. Lett. 85, 5042–5045 (2000)
C.H. Fleming, Hawking radiation as tunneling, Uni. of Maryland. Dept. of Phys., Tech. Rep. (2005)
M. Visser, Some general bounds for one-dimensional scattering. Phys. Rev. A 59, 427–438 (1999)
P. Boonserm, M. Visser, Bounding the bogoliubov coefficients. Ann. Phys. 323, 2779–2798 (2008)
W. Javed, I. Hussain, A. Övgün, Weak deflection angle of Kazakov Solodukhin black hole in plasma medium using Gauss Bonnet theorem and its greybody bonding. Eur. Phys. J. Plus 137, 1–4 (2022)
A. Simpson, M. Visser, JCAP 02, 042 (2019)
K.A. Bronnikov, R.K. Walia, Field sources for Simpson-Visser spacetimes. Phys. Rev. D 105, 044039 (2022)
B.F. Schutz, C.M. Will, Black hole normal modes: a semianalytic approach. Astrophys. J. Lett. 291, L33–L36 (1985)
S. Iyer, C.M. Will, Black hole normal modes: a WKB approach. 1. Foundations and application of a higher order WKB analysis of potential barrier scattering. Phys. Rev. D 35, 3621 (1987)
S. Iyer, Black hole normal modes: a WKB approach. 2. Schwarzschild black holes. Phys. Rev. D 35, 3632 (1987)
R.A. Konoplya, Quasinormal behavior of the d-dimensional Schwarzschild black hole and higher order WKB approach Phys. Rev. D 68, 024018 (2003)
J. Matyjasek, M. Opala, Quasinormal modes of black holes: the improved semianalytic approach. Phys. Rev. D 96, 024011 (2017)
R.A. Konoplya, A. Zhidenko, A.F. Zinhailo, Higher order WKB formula for quasinormal modes and grey-body factors: recipes for quick and accurate calculations. Class. Quantum Gravity 36, 155002 (2019)
K. Destounis, R.P. Macedo, E. Berti, V. Cardoso, J.L. Jaramillo, Pseudospectrum of Reissner-Nordström black holes: quasinormal mode instability and universality. [arXiv:2107.09673 [gr-qc]]
J.D. Bekenstein black hole thermodynamics, Phys. Today 24 (1980)
C. Kiefer. Classical and Quantum black holes (1999)
P. Boonserm, Rigorous bounds on transmission, reflection and bogoliubov coefficients, Ph.D. thesis, Victoria Uni. Wellington (2009)
Author information
Authors and Affiliations
Corresponding author
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
Jha, S.K. Photonsphere, shadow, quasinormal modes, and greybody bounds of non-rotating Simpson–Visser black hole. Eur. Phys. J. Plus 138, 757 (2023). https://doi.org/10.1140/epjp/s13360-023-04384-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/s13360-023-04384-5