Gravitational Quasinormal Modes and Grey-Body Factors of Bonanno-Reuter Regular Black Holes

Abstract

We study gravitational perturbations of the Bonanno--Reuter quantum-corrected black hole arising in the asymptotic safety scenario, focusing on QNMs and grey-body factors. Assuming the RG parameter ω~is fixed to its phenomenologically motivated value, we treat the interpolation parameter γ as free and investigate how it modifies the black hole's response to axial gravitational perturbations. Quasinormal frequencies are computed using the sixth-order WKB method with Padé approximants, and their dependence on γ and the black hole mass M is analyzed. We find that the Schwarzschild limit is rapidly recovered for large M or large γ, while significant deviations arise in the quantum regime. The accuracy of the WKB results is confirmed by time-domain integration of the wave equation. Comparison of grey-body factors computed via both the WKB method and the quasinormal mode correspondence are in a good concordance. Our findings indicate that quantum corrections can leave significant imprints in the ringdown and radiation spectra, while preserving consistency with classical results in the appropriate limit.

Keywords

gravitation / quasinormal modes / black holes / grey-body factors / bonanno-reuter black hole

References

[1] Kokkotas K.D.; Schmidt B.G. Quasinormal modes of stars and black holes. Living Rev. Rel. 1999, 2, 2.

[2] Berti E.; Cardoso V.; Starinets A.O. Quasinormal modes of black holes and black branes. Class. Quant. Grav. 2009, 26, 163001,

[3] Konoplya R.A.; Zhidenko A. Quasinormal modes of black holes: From astrophysics to string theory. Rev. Mod. Phys. 2011, 83, 793-836.

[4] Bolokhov S.V.; Skvortsova M. Review of analytic results on quasinormal modes of black holes. arXiv 2025, arXiv:2504.05014.

[5] Page D.N. Particle Emission Rates from a Black Hole: Massless Particles from an Uncharged, Nonrotating Hole. Phys. Rev. D 1976, 13, 198-206.

[6] Kanti P. Black holes in theories with large extra dimensions: A Review. Int. J. Mod. Phys. A 2004, 19, 4899-4951.

[7] Hawking S.W. Particle Creation by Black Holes. Commun. Math. Phys. 1975, 43, 199-220. Erratum: Commun. Math. Phys. 1976, 46, 206.

[8] Niedermaier M.; Reuter M. The Asymptotic Safety Scenario in Quantum Gravity. Living Rev. Rel. 2006, 9, 5-173.

[9] Bonanno A.; Reuter M. Renormalization group improved black hole space-times. Phys. Rev. D 2000, 62, 043008.

[10] Konoplya R.A.; Zinhailo A.F.; Kunz J.; et al. Quasinormal ringing of regular black holes in asymptotically safe gravity: the importance of overtones. JCAP 2022, 10, 91.

[11] Rincón A.; Panotopoulos G. Quasinormal modes of an improved Schwarzschild black hole. Phys. Dark Univ. 2020, 30, 100639.

[12] Liu D.J.; Yang B.; Zhai Y.J.; et al. Quasinormal modes for asymptotic safe black holes. Class. Quant. Grav. 2012, 29, 145009.

[13] Li J.; Zhong Y. Quasinormal Modes for Electromagnetic Field Perturbation of the Asymptotic Safe Black Hole. Int. J. Theor. Phys. 2013, 52, 1583-1587.

[14] Bouhmadi-López M.; Brahma S.; Chen C.Y.; et al. A consistent model of non-singular Schwarzschild black hole in loop quantum gravity and its quasinormal modes. JCAP 2020, 7, 66.

[15] Regge T.; Wheeler J.A. Stability of a Schwarzschild singularity. Phys. Rev. 1957, 108, 1063-1069.

[16] Konoplya R.A.; Stashko O.S. Probing the effective quantum gravity via quasinormal modes and shadows of black holes. Phys. Rev. D 2025, 111, 104055.

[17] Schutz B.F.; Will C.M. Black hole normal modes: A semianalytic approach. Astrophys. J. Lett. 1985, 291, L33-L36.

[18] Iyer S.; Will C.M. Black Hole Normal Modes: A WKB Approach. 1. Foundations and Application of a Higher Order WKB Analysis of Potential Barrier Scattering. Phys. Rev. D 1987, 35, 3621.

[19] Konoplya R.A. Quasinormal behavior of the d-dimensional Schwarzschild black hole and higher order WKB approach. Phys. Rev. D 2003, 68, 024018.

[20] Matyjasek J.; Opala M. Quasinormal modes of black holes. The improved semianalytic approach. Phys. Rev. D 2017, 96, 024011.

[21] Bolokhov S.V. Long-lived quasinormal modes and oscillatory tails of the Bardeen spacetime. Phys. Rev. D 2024, 109, 064017.

[22] Bolokhov S.V. Late time decay of scalar and Dirac fields around an asymptotically de Sitter black hole in the Eu- ler-Heisenberg electrodynamics. Eur. Phys. J. C 2024, 84, 634.

[23] Skvortsova M. Ringing of Extreme Regular Black Holes. Grav. Cosmol. 2024, 30, 279-288.

[24] Skvortsova M. Quasinormal Spectrum of (2+1)-Dimensional Asymptotically Flat, dS and AdS Black Holes. Fortsch. Phys. 2024, 72, 2400036.

[25] Gundlach C.; Price R.H.; Pullin J. Late time behavior of stellar collapse and explosions: 1. Linearized perturbations. Phys. Rev. D 1994, 49, 883-889.

[26] Konoplya R.A.; Zhidenko A.; Zinhailo A.F. Higher order WKB formula for quasinormal modes and grey-body factors: recipes for quick and accurate calculations. Class. Quant. Grav. 2019, 36, 155002.

[27] Konoplya R.A.; Zhidenko A. Correspondence between grey-body factors and quasinormal modes. JCAP 2024, 09, 068.

[28] Bolokhov S.V.; Skvortsova M. Correspondence between quasinormal modes and grey-body factors of spherically symmetric traversable wormholes. JCAP 2025, 4, 25.

[29] Skvortsova M. Quantum corrected black holes: testing the correspondence between grey-body factors and quasinormal modes. arXiv 2024, arXiv:2411.06007.

[30] Dubinsky A. Grey-body factors for gravitational and electromagnetic perturbations around Gibbons-Maeda-Garfinkle- Horovits-Strominger black holes. arXiv 2024, arXiv:2412.00625.

[31] Malik Z. Correspondence between quasinormal modes and grey-body factors for massive fields in Schwarzschild-de Sitter spacetime. JCAP 2025, 4, 42.

[32] Lütfüolu B.C. Quasinormal Modes and Gray-Body Factors for Gravitational Perturbations in Asymptotically Safe Gravity. arXiv 2025, arXiv:2505.06966.

[33] Lütfüolu B.C. Non-minimal Einstein-Yang-Mills black holes: fundamental quasinormal mode and grey-body factors versus outburst of overtones. Eur. Phys. J. C 2025, 85, 630.

[34] Lütfüolu B.C. Long-lived quasinormal modes and gray-body factors of black holes and wormholes in dark matter inspired Weyl gravity. Eur. Phys. J. C 2025, 85, 486.

[35] Konoplya R.A.; Stuchlik Z.; Zhidenko A.; Zinhailo A.F. Quasinormal modes of renormalization group improved Dymnikova regular black holes. Phys. Rev. D 2023, 107, 104050.

[36] Zinhailo A.F. Quasinormal spectrum in the asymptotically safe gravity. arXiv 2023, arXiv:2311.05380.

[37] Stashko O. Quasinormal modes and gray-body factors of regular black holes in asymptotically safe gravity. Phys. Rev. D 2024, 110, 084016.