Abstract
We investigated the superradiance and stability of the regularized 4D charged Einstein-Gauss-Bonnet black hole which is recently inspired by Glavan and Lin [Phys. Rev. Lett. 124, 081301 (2020)]. We found that the positive Gauss-Bonnet coupling constant α enhances the superradiance, while the negative α suppresses it. The condition for superradiant instability is proved. We also worked out the quasinormal modes (QNMs) of the charged Einstein-Gauss-Bonnet black hole and found that the real part of all the QNMs does not satisfy the superradiance condition and the imaginary parts are all negative. Therefore this black hole is stable. When α makes the black hole extremal, there are normal modes.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R. Penrose and R.M. Floyd, Extraction of rotational energy from a black hole, Nature 229 (1971) 177 [INSPIRE].
Y.B. Zel’dovich, Amplification of Cylindrical Electromagnetic Waves Reflected from a Rotating Body, Sov. Phys. JETP 35 (1972) 1085.
A.A. Starobinsky, Amplification of waves reflected from a rotating “black hole”, Sov. Phys. JETP 37 (1973) 28 Zh. Eksp. Teor. Fiz. 64 (1973) 48 [INSPIRE].
W.H. Press and S.A. Teukolsky, Floating Orbits, Superradiant Scattering and the Black-hole Bomb, Nature 238 (1972) 211 [INSPIRE].
J.D. Bekenstein, Extraction of energy and charge from a black hole, Phys. Rev. D 7 (1973) 949 [INSPIRE].
S.W. Hawking and H.S. Reall, Charged and rotating AdS black holes and their CFT duals, Phys. Rev. D 61 (2000) 024014 [hep-th/9908109] [INSPIRE].
R. Brito, V. Cardoso and P. Pani, Superradiance: Energy Extraction, Black-Hole Bombs and Implications for Astrophysics and Particle Physics, vol. 906, Springer (2015), DOI [arXiv:1501.06570] [INSPIRE].
L. Di Menza and J.-P. Nicolas, Superradiance on the Reissner-Nordstrøm metric, Class. Quant. Grav. 32 (2015) 145013 [arXiv:1411.3988] [INSPIRE].
M. Richartz and A. Saa, Challenging the weak cosmic censorship conjecture with charged quantum particles, Phys. Rev. D 84 (2011) 104021 [arXiv:1109.3364] [INSPIRE].
Y.S. Myung, Instability of rotating black hole in a limited form of f (R) gravity, Phys. Rev. D 84 (2011) 024048 [arXiv:1104.3180] [INSPIRE].
Y.S. Myung, Instability of a Kerr black hole in f (R) gravity, Phys. Rev. D 88 (2013) 104017 [arXiv:1309.3346] [INSPIRE].
C.-Y. Zhang, S.-J. Zhang and B. Wang, Superradiant instability of Kerr-de Sitter black holes in scalar-tensor theory, JHEP 08 (2014) 011 [arXiv:1405.3811] [INSPIRE].
C.-Y. Zhang, S.-J. Zhang and B. Wang, Charged scalar perturbations around Garfinkle-Horowitz-Strominger black holes, Nucl. Phys. B 899 (2015) 37 [arXiv:1501.03260] [INSPIRE].
M.F. Wondrak, P. Nicolini and J.W. Moffat, Superradiance in Modified Gravity (MOG), JCAP 12 (2018) 021 [arXiv:1809.07509] [INSPIRE].
M. Khodadi, A. Talebian and H. Firouzjahi, Black Hole Superradiance in f(R) Gravities, arXiv:2002.10496 [INSPIRE].
T. Clifton, P.G. Ferreira, A. Padilla and C. Skordis, Modified Gravity and Cosmology, Phys. Rept. 513 (2012) 1 [arXiv:1106.2476] [INSPIRE].
D. Glavan and C. Lin, Einstein-Gauss-Bonnet Gravity in Four-Dimensional Spacetime, Phys. Rev. Lett. 124 (2020) 081301 [arXiv:1905.03601] [INSPIRE].
R.-G. Cai, L.-M. Cao and N. Ohta, Black Holes in Gravity with Conformal Anomaly and Logarithmic Term in Black Hole Entropy, JHEP 04 (2010) 082 [arXiv:0911.4379] [INSPIRE].
Y. Tomozawa, Quantum corrections to gravity, arXiv:1107.1424 [INSPIRE].
G. Cognola, R. Myrzakulov, L. Sebastiani and S. Zerbini, Einstein gravity with Gauss-Bonnet entropic corrections, Phys. Rev. D 88 (2013) 024006 [arXiv:1304.1878] [INSPIRE].
R.A. Konoplya and A.F. Zinhailo, Quasinormal modes, stability and shadows of a black hole in the novel 4D Einstein-Gauss-Bonnet gravity, arXiv:2003.01188 [INSPIRE].
R.A. Konoplya and A. Zhidenko, Black holes in the four-dimensional Einstein-Lovelock gravity, Phys. Rev. D 101 (2020) 084038 [arXiv:2003.07788] [INSPIRE].
R.A. Konoplya and A. Zhidenko, BTZ black holes with higher curvature corrections in the 3D Einstein-Lovelock theory, arXiv:2003.12171 [INSPIRE].
R.A. Konoplya and A. Zhidenko, (In)stability of black holes in the 4D Einstein-Gauss-Bonnet and Einstein-Lovelock gravities, Phys. Dark Univ. 30 (2020) 100697 [arXiv:2003.12492] [INSPIRE].
R.A. Konoplya and A.F. Zinhailo, Grey-body factors and Hawking radiation of black holes in 4D Einstein-Gauss-Bonnet gravity, arXiv:2004.02248 [INSPIRE].
M. Guo and P.-C. Li, Innermost stable circular orbit and shadow of the 4D Einstein-Gauss-Bonnet black hole, Eur. Phys. J. C 80 (2020) 588 [arXiv:2003.02523] [INSPIRE].
C.-Y. Zhang, P.-C. Li and M. Guo, Greybody factor and power spectra of the Hawking radiation in the novel 4D Einstein-Gauss-Bonnet de-Sitter gravity, arXiv:2003.13068 [INSPIRE].
P.G.S. Fernandes, Charged Black Holes in AdS Spaces in 4D Einstein Gauss-Bonnet Gravity, Phys. Lett. B 805 (2020) 135468 [arXiv:2003.05491] [INSPIRE].
A. Casalino, A. Colleaux, M. Rinaldi and S. Vicentini, Regularized Lovelock gravity, arXiv:2003.07068 [INSPIRE].
H. Lü and Y. Pang, Horndeski Gravity as D → 4 Limit of Gauss-Bonnet, arXiv:2003.11552 [INSPIRE].
T. Kobayashi, Effective scalar-tensor description of regularized Lovelock gravity in four dimensions, JCAP 07 (2020) 013 [arXiv:2003.12771] [INSPIRE].
S.-W. Wei and Y.-X. Liu, Testing the nature of Gauss-Bonnet gravity by four-dimensional rotating black hole shadow, arXiv:2003.07769 [INSPIRE].
Y.-P. Zhang, S.-W. Wei and Y.-X. Liu, Spinning test particle in four-dimensional Einstein-Gauss-Bonnet Black Hole, Universe 6 (2020) 103 [arXiv:2003.10960] [INSPIRE].
S.-W. Wei and Y.-X. Liu, Extended thermodynamics and microstructures of four-dimensional charged Gauss-Bonnet black hole in AdS space, Phys. Rev. D 101 (2020) 104018 [arXiv:2003.14275] [INSPIRE].
K. Hegde, A. Naveena Kumara, C.L.A. Rizwan, A.K.M. and M.S. Ali, Thermodynamics, Phase Transition and Joule Thomson Expansion of novel 4-D Gauss Bonnet AdS Black Hole, arXiv:2003.08778 [INSPIRE].
D.V. Singh and S. Siwach, Thermodynamics and P-v criticality of Bardeen-AdS Black Hole in 4-D Einstein-Gauss-Bonnet Gravity, Phys. Lett. B 808 (2020) 135658 [arXiv:2003.11754] [INSPIRE].
S.A. Hosseini Mansoori, Thermodynamic geometry of the novel 4-D Gauss Bonnet AdS Black Hole, arXiv:2003.13382 [INSPIRE].
C. Liu, T. Zhu and Q. Wu, Thin Accretion Disk around a four-dimensional Einstein-Gauss-Bonnet Black Hole, arXiv:2004.01662 [INSPIRE].
R. Kumar and S.G. Ghosh, Rotating black holes in 4D Einstein-Gauss-Bonnet gravity and its shadow, JCAP 20 (2020) 053 [arXiv:2003.08927] [INSPIRE].
S.G. Ghosh and S.D. Maharaj, Radiating black holes in the novel 4D Einstein-Gauss-Bonnet gravity, Phys. Dark Univ. 30 (2020) 100687 [arXiv:2003.09841] [INSPIRE].
S.G. Ghosh and R. Kumar, Generating black holes in the novel 4D Einstein-Gauss-Bonnet gravity, arXiv:2003.12291 [INSPIRE].
D.V. Singh, S.G. Ghosh and S.D. Maharaj, Clouds of string in the novel 4D Einstein-Gauss-Bonnet black holes, arXiv:2003.14136 [INSPIRE].
A. Kumar and S.G. Ghosh, Hayward black holes in the novel 4D Einstein-Gauss-Bonnet gravity, arXiv:2004.01131 [INSPIRE].
S.U. Islam, R. Kumar and S.G. Ghosh, Gravitational lensing by black holes in 4D Einstein-Gauss-Bonnet gravity, arXiv:2004.01038 [INSPIRE].
A. Kumar and R. Kumar, Bardeen black holes in the novel 4D Einstein-Gauss-Bonnet gravity, arXiv:2003.13104 [INSPIRE].
D.D. Doneva and S.S. Yazadjiev, Relativistic stars in 4D Einstein-Gauss-Bonnet gravity, arXiv:2003.10284 [INSPIRE].
S. Nojiri and S.D. Odintsov, Novel cosmological and black hole solutions in Einstein and higher-derivative gravity in two dimensions, EPL 130 (2020) 10004 [arXiv:2004.01404] [INSPIRE].
M.S. Churilova, Quasinormal modes of the Dirac field in the novel 4D Einstein-Gauss-Bonnet gravity, arXiv:2004.00513 [INSPIRE].
A.K. Mishra, Quasinormal modes and Strong Cosmic Censorship in the novel 4D Einstein-Gauss-Bonnet gravity, arXiv:2004.01243 [INSPIRE].
S.-L. Li, P. Wu and H. Yu, Stability of the Einstein Static Universe in 4D Gauss-Bonnet Gravity, arXiv:2004.02080 [INSPIRE].
M. Heydari-Fard, M. Heydari-Fard and H.R. Sepangi, Bending of light in novel 4D Gauss-Bonnet-de Sitter black holes by Rindler-Ishak method, arXiv:2004.02140 [INSPIRE].
X.-H. Jin, Y.-X. Gao and D.-J. Liu, Strong gravitational lensing of a 4-dimensional Einstein-Gauss-Bonnet black hole in homogeneous plasma, Int. J. Mod. Phys. D 29 (2020) 2050065 [arXiv:2004.02261] [INSPIRE].
W.-Y. Ai, A note on the novel 4D Einstein-Gauss-Bonnet gravity, Commun. Theor. Phys. 72 (2020) 095402 [arXiv:2004.02858] [INSPIRE].
K. Aoki, M.A. Gorji and S. Mukohyama, A consistent theory of D → 4 Einstein-Gauss-Bonnet gravity, arXiv:2005.03859 [INSPIRE].
K. Aoki, M.A. Gorji and S. Mukohyama, Cosmology and gravitational waves in consistent D → 4 Einstein-Gauss-Bonnet gravity, arXiv:2005.08428 [INSPIRE].
H.T. Cho, A.S. Cornell, J. Doukas and W. Naylor, Black hole quasinormal modes using the asymptotic iteration method, Class. Quant. Grav. 27 (2010) 155004 [arXiv:0912.2740] [INSPIRE].
H.T. Cho, A.S. Cornell, J. Doukas, T.R. Huang and W. Naylor, A New Approach to Black Hole Quasinormal Modes: A Review of the Asymptotic Iteration Method, Adv. Math. Phys. 2012 (2012) 281705 [arXiv:1111.5024] [INSPIRE].
T. Pappas, P. Kanti and N. Pappas, Hawking radiation spectra for scalar fields by a higher-dimensional Schwarzschild-de Sitter black hole, Phys. Rev. D 94 (2016) 024035 [arXiv:1604.08617] [INSPIRE].
J. Ahmed and K. Saifullah, Greybody factor of a scalar field from Reissner-Nordström-de Sitter black hole, Eur. Phys. J. C 78 (2018) 316 [arXiv:1610.06104] [INSPIRE].
C.-Y. Zhang, P.-C. Li and B. Chen, Greybody factors for a spherically symmetric Einstein-Gauss-Bonnet-de Sitter black hole, Phys. Rev. D 97 (2018) 044013 [arXiv:1712.00620] [INSPIRE].
P.-C. Li and C.-Y. Zhang, Hawking radiation for scalar fields by Einstein-Gauss-Bonnet-de Sitter black holes, Phys. Rev. D 99 (2019) 024030 [arXiv:1901.05749] [INSPIRE].
J. Grain, A. Barrau and P. Kanti, Exact results for evaporating black holes in curvature-squared lovelock gravity: Gauss-Bonnet greybody factors, Phys. Rev. D 72 (2005) 104016 [hep-th/0509128] [INSPIRE].
T. Harmark, J. Natario and R. Schiappa, Greybody Factors for d-Dimensional Black Holes, Adv. Theor. Math. Phys. 14 (2010) 727 [arXiv:0708.0017] [INSPIRE].
R.A. Konoplya and A. Zhidenko, Quasinormal modes of black holes: From astrophysics to string theory, Rev. Mod. Phys. 83 (2011) 793 [arXiv:1102.4014] [INSPIRE].
R.L.H.H. Ciftci and N. Saad, Asymptotic iteration method for eigenvalue problems, J. Phys. A 36 (2003) 11807 [math-ph/0309066].
H. Ciftci, R.L. Hall and N. Saad, Perturbation theory in a framework of iteration methods, Phys. Lett. A 340 (2005) 388 [math-ph/0504056] [INSPIRE].
J.C. Degollado and C.A.R. Herdeiro, Stationary scalar configurations around extremal charged black holes, Gen. Rel. Grav. 45 (2013) 2483 [arXiv:1303.2392] [INSPIRE].
M.O.P. Sampaio, C. Herdeiro and M. Wang, Marginal scalar and Proca clouds around Reissner-Nordström black holes, Phys. Rev. D 90 (2014) 064004 [arXiv:1406.3536] [INSPIRE].
S.-J. Zhang, Q. Pan, B. Wang and E. Abdalla, Horizon instability of massless scalar perturbations of an extreme Reissner-Nordström-AdS black hole, JHEP 09 (2013) 101 [arXiv:1308.0635] [INSPIRE].
S. Hod, Stability of the extremal Reissner-Nordström black hole to charged scalar perturbations, Phys. Lett. B 713 (2012) 505 [arXiv:1304.6474] [INSPIRE].
S. Hod, Stability of the extremal Reissner-Nordström black hole to charged scalar perturbations, Phys. Lett. B 713 (2012) 505 [arXiv:1304.6474] [INSPIRE].
C.A.R. Herdeiro, J.C. Degollado and H.F. Rúnarsson, Rapid growth of superradiant instabilities for charged black holes in a cavity, Phys. Rev. D 88 (2013) 063003 [arXiv:1305.5513] [INSPIRE].
J.C. Degollado and C.A.R. Herdeiro, Time evolution of superradiant instabilities for charged black holes in a cavity, Phys. Rev. D 89 (2014) 063005 [arXiv:1312.4579] [INSPIRE].
N. Sanchis-Gual, J.C. Degollado, P.J. Montero, J.A. Font and C. Herdeiro, Explosion and Final State of an Unstable Reissner-Nordström Black Hole, Phys. Rev. Lett. 116 (2016) 141101 [arXiv:1512.05358] [INSPIRE].
N. Sanchis-Gual, J.C. Degollado, J.A. Font, C. Herdeiro and E. Radu, Dynamical formation of a hairy black hole in a cavity from the decay of unstable solitons, Class. Quant. Grav. 34 (2017) 165001 [arXiv:1611.02441] [INSPIRE].
Z. Zhu, S.-J. Zhang, C.E. Pellicer, B. Wang and E. Abdalla, Stability of Reissner-Nordström black hole in de Sitter background under charged scalar perturbation, Phys. Rev. D 90 (2014) 044042 [Addendum ibid. 90 (2014) 049904] [arXiv:1405.4931] [INSPIRE].
R.A. Konoplya and A. Zhidenko, Charged scalar field instability between the event and cosmological horizons, Phys. Rev. D 90 (2014) 064048 [arXiv:1406.0019] [INSPIRE].
P. Liu, C. Niu and C.-Y. Zhang, Instability of the novel 4D charged Einstein-Gauss-Bonnet de-Sitter black hole, arXiv:2004.10620 [INSPIRE].
P. Liu, C. Niu and C.-Y. Zhang, Instability of the novel 4D charged Einstein-Gauss-Bonnet de-Sitter black hole, arXiv:2004.10620 [INSPIRE].
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: 2004.03141
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
Zhang, CY., Zhang, SJ., Li, PC. et al. Superradiance and stability of the regularized 4D charged Einstein-Gauss-Bonnet black hole. J. High Energ. Phys. 2020, 105 (2020). https://doi.org/10.1007/JHEP08(2020)105
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2020)105