Journal of Holography Applications in Physics
Hawking-Page Transition from Logarithmic Entropy in f(R) Gravity
Document Type : Regular article
Author
Department of Physics, Jamia Millia Islamia, New Delhi, 110025, India; Department of Computer Sciences, Asian School of Business, Uttar Pradesh, 210303, India
Abstract
We analyze the thermodynamics and phase structure of a static, spherically symmetric black hole that extends Schwarzschild within f(R) gravity. In the extended framework, we include a model-independent, one-loop-motivated logarithmic entropy correction with a free coefficient b. We derive closed-form expressions for temperature, enthalpy, corrected entropy, Gibbs free energy, and heat capacity to first order in the deformation parameter, and chart the Hawking-Page transition and local stability. A positive $b$ suppresses local stability for small black holes, while negative b enhances it. We also state the generalized first law with the f(R) coupling as a thermodynamic variable, providing a practical phenomenology for future microscopic determinations of b.
Keywords
- Black-hole thermodynamics
- Gibbs free energy
- Logarithmic entropy correction
- AdS black holes
- Phase structure and criticality
- Holographic implications
Main Subjects
Article PDF
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[29] M. Faizal, A. Shabir, and A. K. Khan, “Consequences of Gödel theorems on third quantized theories like string field theory and group field theory,” Nucl. Phys. B 1010, 116774 (2025) DOI: 10.1016/j.nuclphysb.2024.116774.
[30] S. W. Hawking, “Zeta Function Regularization of Path Integrals in Curved SpaceTime,” Commun. Math. Phys. 55, 133 (1977) DOI: 10.1007/BF01626516.
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[35] S. Gunasekaran, R. B. Mann, and D. Kubiznak, “Extended phase space thermodynamics for charged and rotating black holes and Born-Infeld vacuum polarization,” JHEP 11, 110 (2012) DOI: 10.1007/JHEP11(2012)110.
[36] E. Spallucci and A. Smailagic, “Maxwell’s equal area law for charged Anti-deSitter black holes,” Phys. Lett. B 723, 436 (2013) DOI: 10.1016/j.physletb.2013.05.038.
[2] S. W. Hawking, “Particle Creation by Black Holes,” Commun. Math. Phys. 43, 199 (1975) DOI: 10.1007/BF02345020.
[3] G. ’t Hooft, “Dimensional reduction in quantum gravity,” Conf. Proc. C 930308, 284 (1993).
[4] L. Susskind, “The World as a hologram,” J. Math. Phys. 36, 6377 (1995) DOI: 10.1063/1.531249.
[5] R. K. Kaul and P. Majumdar, “Logarithmic correction to the Bekenstein-Hawking entropy,” Phys. Rev. Lett. 84, 5255 (2000) DOI: 10.1103/PhysRevLett.84.5255.
[6] S. N. Solodukhin, “Entanglement entropy of black holes,” Living Rev. Rel. 14, 8 (2011) DOI: 10.12942/lrr-2011-8.
[7] A. Sen, “Logarithmic Corrections to Schwarzschild and Other Non-extremal Black Hole Entropy in Different Dimensions,” JHEP 04, 156 (2013) DOI: 10.1007/JHEP04(2013)156.
[8] S. Carlip, “Logarithmic corrections to black hole entropy from the Cardy formula,” Class. Quant. Grav. 17, 4175 (2000) DOI: 10.1088/0264-9381/17/20/302.
[9] A. Strominger, “Black hole entropy from near horizon microstates,” JHEP 02, 009 (1998) DOI: 10.1088/1126-6708/1998/02/009.
[10] S. Das, P. Majumdar, and R. K. Bhaduri, “General logarithmic corrections to black hole entropy,” Class. Quant. Grav. 19, 2355 (2002) DOI: 10.1088/0264-9381/19/9/302.
[11] T. Jacobson, “Thermodynamics of space-time: The Einstein equation of state,” Phys. Rev. Lett. 75, 1260 (1995) DOI: 10.1103/PhysRevLett.75.1260.
[12] T. P. Sotiriou and V. Faraoni, “f(R) Theories Of Gravity,” Rev. Mod. Phys. 82, 451 (2010) DOI: 10.1103/RevModPhys.82.451.
[13] A. De Felice and S. Tsujikawa, “f(R) theories,” Living Rev. Rel. 13, 3 (2010) DOI: 10.12942/lrr-2010-3.
[14] G. G. L. Nashed, “Extension of the Schwarzschild black hole solution in f(R) gravitational theory and its physical properties,” Eur. Phys. J. C 84, 5 (2024) DOI: 10.1140/epjc/s10052-023-12349-2.
[15] D. Kastor, S. Ray, and J. Traschen, “Enthalpy and the Mechanics of AdS Black Holes,” Class. Quant. Grav. 26, 195011 (2009) DOI: 10.1088/0264-9381/26/19/195011.
[16] D. Kubiznak and R. B. Mann, “P-V criticality of charged AdS black holes,” JHEP 07, 033 (2012) DOI: 10.1007/JHEP07(2012)033.
[17] R. M. Wald, “Black hole entropy is the Noether charge,” Phys. Rev. D 48, R3427 (1993) DOI: 10.1103/PhysRevD.48.R3427.
[18] R. B. Mann, B. Pourhassan, and P. Rudra, “Note on the thermodynamic stability of a black ring at quantum scales,” Phys. Rev. D 103, 066015 (2021) DOI: 10.1103/PhysRevD.103.066015.
[19] B. Pourhassan, M. Faizal, Z. Zaz, and A. Bhat, “Quantum fluctuations of a BTZ black hole in massive gravity,” Phys. Lett. B 773, 325 (2017) DOI: 10.1016/j.physletb.2017.08.046.
[20] B. Pourhassan, M. Faizal, S. Upadhyay, and L. A. Asfar, “Thermal Fluctuations in a Hyperscaling Violation Background,” Eur. Phys. J. C 77, 555 (2017) DOI: 10.1140/epjc/s10052-017-5125-x.
[21] B. Pourhassan, S. Upadhyay, H. Saadat, and H. Farahani, “Quantum gravity effects on Hořava-Lifshitz black hole,” Nucl. Phys. B 928, 415 (2018) DOI: 10.1016/j.nuclphysb.2018.01.018.
[22] B. Pourhassan and M. Faizal, “Thermodynamics of a suffcient small singly spinning Kerr-AdS black hole,” Nucl. Phys. B 913, 834 (2016) DOI: 10.1016/j.nuclphysb.2016.10.013.
[23] M. Faizal and B. Pourhassan, “Correction terms for the thermodynamics of a black Saturn,” Phys. Lett. B 751, 487 (2015) DOI: 10.1016/j.physletb.2015.10.077.
[24] S. W. Hawking and D. N. Page, “Thermodynamics of Black Holes in anti-De Sitter Space,” Commun. Math. Phys. 87, 577 (1983) DOI: 10.1007/BF01208266.
[25] M. Faizal, A. Shabir, and A. K. Khan, “Application of Chaitin’s Incompleteness Theorem to Quantum Gravity,” Int. J. Theor. Phys. 64, 194 (2025) DOI: 10.1007/s10773- 025-06065-8.
[26] M. Faizal, L. M. Krauss, A. Shabir, and F. Marino, “Consequences of Undecidability in Physics on the Theory of Everything,” JHAP 5, 10 (2025) DOI: 10.22128/jhap.2025.1024.1118.
[27] M. Faizal, A. Shabir, and A. K. Khan, “Consequences of Gödel’s Theorems on Quantum Gravity,” Int. J. Theor. Phys. 63, 290 (2024) DOI: 10.1007/s10773-024-05818-1.
[28] M. Faizal, A. Shabir, and A. K. Khan, “Implications of Tarski’s undefinability theorem on the Theory of Everything,” EPL 148, 39001 (2024) DOI: 10.1209/0295- 5075/ad80c2.
[29] M. Faizal, A. Shabir, and A. K. Khan, “Consequences of Gödel theorems on third quantized theories like string field theory and group field theory,” Nucl. Phys. B 1010, 116774 (2025) DOI: 10.1016/j.nuclphysb.2024.116774.
[30] S. W. Hawking, “Zeta Function Regularization of Path Integrals in Curved SpaceTime,” Commun. Math. Phys. 55, 133 (1977) DOI: 10.1007/BF01626516.
[31] D. V. Vassilevich, “Heat kernel expansion: User’s manual,” Phys. Rept. 388, 279 (2003) DOI: 10.1016/j.physrep.2003.09.002.
[32] D. V. Fursaev and S. N. Solodukhin, “On the description of the Riemannian geometry in the presence of conical defects,” Phys. Rev. D 52, 2133 (1995) DOI: 10.1103/PhysRevD.52.2133.
[33] A. Chamblin, R. Emparan, C. V. Johnson, and R. C. Myers, “Charged AdS black holes and catastrophic holography,” Phys. Rev. D 60, 064018 (1999) DOI: 10.1103/PhysRevD.60.064018.
[34] M. M. Caldarelli, G. Cognola, and D. Klemm, “Thermodynamics of Kerr-NewmanAdS black holes and conformal field theories,” Class. Quant. Grav. 17, 399 (2000) DOI: 10.1088/0264-9381/17/2/310.
[35] S. Gunasekaran, R. B. Mann, and D. Kubiznak, “Extended phase space thermodynamics for charged and rotating black holes and Born-Infeld vacuum polarization,” JHEP 11, 110 (2012) DOI: 10.1007/JHEP11(2012)110.
[36] E. Spallucci and A. Smailagic, “Maxwell’s equal area law for charged Anti-deSitter black holes,” Phys. Lett. B 723, 436 (2013) DOI: 10.1016/j.physletb.2013.05.038.
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Volume 6, Issue 1
December 2025Pages 60-81
- Receive Date: 28 September 2025
- Revise Date: 11 October 2025
- Accept Date: 28 October 2025