Journal of Holography Applications in Physics
Quantum gravitational corrected evolution equations of charged black holes
Document Type : Regular article
Author
Bethe Center for Theoretical Physics, University of Bonn, Germany
Abstract
We explain how quantum gravity, treated as an effective field theory, might modify the evaporative evolution of a four-dimensional, non-extremal, non-rotating, charged black hole. With some approximations, we derive a set of coupled differential equations describing the charge and mass of the black hole as a function of time. These equations represent a generalisation of the analogous ones already present in the literature for classical black holes.
Keywords
Main Subjects
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[2] Jacob D. Bekenstein ”Black holes and entropy”, Phys. Rev. D 7, 2333–2346 (1973).
[3] S. Das, P. Majumdar, R. K. Bhaduri, ”General logarithmic corrections to black hole entropy”, Class. Quant. Grav. 19, 2355–2368 (2002).
[4] B. Pourhassan, B. and M. Faizal, ”Thermal Fluctuations in a Charged AdS Black Hole”, EPL 111, 40006 (2015).
[5] A. Chatterjee, and A. Ghosh, ”Exponential Corrections to Black Hole Entropy”, Phys. Rev. Lett. 125, 041302 (2020).
[6] B. Pourhassan, ”Exponential corrected thermodynamics of black holes”, J. Stat. Mech. 2107, 073102 (2021).
[7] S. Upadhyay, N. ul islam and Prince A. Ganai, ”A modified thermodynamics of rotating and charged BTZ black hole”, JHAP 2, (1) 25–48 (2022).
[8] X. Calmet, and F. Kuipers, ”Quantum gravitational corrections to the entropy of a Schwarzschild black hole”, Phys. Rev. D 104, 066012 (2021).
[9] R. M. Wald, ”Black hole entropy is the Noether charge”, Phys. Rev. D 48, R3427–R3431 (1993).
[10] R. C. Delgado, ”Quantum gravitational corrections to the entropy of a Reissner–Nordstr¨om black hole”, Eur. Phys. J. C 82, 272 (2022).
[11] W. A. Hiscock and L. D. Weems, Evolution of Charged Evaporating Black Holes, Phys. Rev. D 41, 1142 (1990).
[12] S. Weinberg, Ultraviolet divergences in quantum theories of gravitation, in General Relativity: An Einstein Centenary Survey, pp. 790831. Univ. Pr., Cambridge, UK, 1980.
[13] A. A. Starobinsky, Evolution of small perturbations of isotropic cosmological models with one-loop quantum gravitational corrections, JETP Lett. 34, 438441 (1981).
[14] A. O. Barvinsky and G. A. Vilkovisky, The generalized Schwinger-DeWitt technique and the unique effective action in quantum gravity, Phys. Lett. B 131, 313318 (1983).
[15] A. O. Barvinsky and G. A. Vilkovisky, The Generalized Schwinger-DeWitt Technique in Gauge Theories and Quantum Gravity, Phys. Rept. 119, 174 (1985).
[16] A. O. Barvinsky and G. A. Vilkovisky, Beyond the Schwinger-Dewitt Technique: Converting Loops Into Trees and In-In Currents, Nucl. Phys. B 282, 163188 (1987).
[17] A. O. Barvinsky and G. A. Vilkovisky, Covariant perturbation theory. 2: Second order in the curvature. General algorithms, Nucl. Phys. B 333, 471511 (1990).
[18] J. F. Donoghue, General relativity as an effective feld theory: The leading quantum corrections, Phys. Rev. D 50, 38743888 (1994).
[19] R. Myrzakulov, S. Odintsov, and L. Sebastiani, Inflationary universe from higher-derivative quantum gravity, Phys. Rev. D 91 no. 8, 083529 (2015).
[20] E. Elizalde, S. D. Odintsov, L. Sebastiani, and R. Myrzakulov, Beyond-one-loop quantum gravity action yielding both inflation and late-time acceleration, Nucl. Phys. B 921, 411435 (2017).
[21] J. F. Donoghue and B. K. El-Menouf, Nonlocal quantum effects in cosmology: Quantum memory, nonlocal FLRW equations, and singularity avoidance, Phys. Rev. D 89 no. 10, 104062 (2014).
[22] J. F. Donoghue and B. K. El-Menouf, Covariant non-local action for massless QED and the curvature expansion, JHEP 10, 044 (2015).
[23] B. K. El-Menouf, Quantum gravity of Kerr-Schild spacetimes and the logarithmic correction to Schwarzschild black hole entropy, JHEP 05, 035 (2016).
[24] J. S. Schwinger, On gauge invariance and vacuum polarization, Phys. Rev. 82, 664679 (1951).
[25] S. P. Gavrilov and D. M. Gitman, Vacuum instability in external felds, Phys. Rev. D 53, 71627175 (1996).
[26] H. Xu, Y. C. Ong, and M.-H. Yung, Cosmic Censorship and the Evolution of d-Dimensional Charged Evaporating Black Holes, Phys. Rev. D 101 no. 6, 064015 (2020).
[27] L. C. B. Crispino, S. R. Dolan, and E. S. Oliveira, Scattering of massless scalar waves by Reissner–Nordstr¨om black holes, Phys. Rev. D 79, 064022 (2009).
[28] H. Xu and M.-H. Yung, Black hole evaporation in Lovelock gravity with diverse dimensions, Phys. Lett. B 794, 7782 (2019).
[29] D. N. Page, Particle Emission Rates from a Black Hole. 2. Massless Particles from a Rotating Hole, Phys. Rev. D 14, 32603273 (1976).
[30] G. S´arosi, AdS2 holography and the SYK model, PoS Modave2017, 001 (2018).
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Volume 3, Issue 1
March 2023Pages 39-48
- Receive Date: 10 January 2023
- Revise Date: 10 February 2023
- Accept Date: 17 February 2023