Journal of Holography Applications in Physics
Regular Black Holes in Einstein-Gauss-Bonnet Gravity Coupled with a Cloud of Strings
Document Type : Regular article
Authors
1 Department Physics, Hansraj College, University of Delhi, New Delhi, 110007 India
2 Department Physics, Goverment degree College, Unnao, Uttar Pradesh, India
3 Department of Civil Engineering, Faculty of Engineering, Marwadi University, Rajkot, Gujarat 360003, India
Abstract
In this paper, we construct regular black holes coupled with the Cloud of String, which becomes Maxwell's theory in the weak field limit, and we can compare new attributes against the standard Letelier black hole and Schwarzschild black hole. The thermodynamic quantities associated with the black hole are modified in the presence of CoS. We also study the global properties of the solutions and derive the corrected first law of thermodynamics. In addition, we also study the local and global stability of the black hole solution.
Keywords
Main Subjects
Article PDF
[1] A.D. Sakharov, ”The Initial Stage of an Expanding Universe and the Appearance of a Nonuniform Distribution of Matter” Sov. Phys. JETP,22, 241 (1966).
[2] E.B. Gliner, ”Algebraic Properties of the Energy-momentum Tensor and Vacuum-like States o+ Matter” Sov. Phys. JETP, 22, 378 (1966).
[3] J. Bardeen, ”Non-singular general relativistic gravitational collapse” in Proceedings of GR5 (Tiflis, U.S.S.R., 1968).
[4] E. Ayon-Beato, A. Garcia,”The Bardeen Model as a Nonlinear Magnetic Monopole”, Phys. Lett. B 493, 149 (2000) DOI: https://doi.org/10.1016/S0370-2693(00)01125-4
[5] E. Ayon-Beato and A. Garcia, ”Non-Singular Charged Black Hole Solution for Non-Linear Source”,Gen. Relativ. Gravit. 31, 629 (1999). DOI: https://doi.org/10.1023/A:1026640911319
[6] E. Ayon-Beato and A. Garcia, ”Four Parametric Regular Black Hole Solution”, Gen. Relativ. Gravit.37, 635(2005). DOI: https://doi.org/10.1007/s10714-005-0050-y
[7] E. Ayon-Beato and A. Garcia, ”Regular black hole in general relativity coupled to nonlinear electrodynamics”, Phys. Rev. Lett. 80, 5056 (1998). DOI: https://doi.org/10.1103/PhysRevLett.80.5056
[8] R. G. Daghigh and M. D. Green, ”Gravitational and electromagnetic radiation from an electrically charged black hole in general nonlinear electrodynamics” Phys. Rev. D 105, 024055 (2022). DOI: https://doi.org/10.1103/PhysRevD.105.024055
[9] D. V. Singh, S. G. Ghosh and S. D. Maharaj, ”Exact nonsingular black holes and thermodynamics”, Nucl. Phys. B 981 (2022), 115854. DOI: 10.1016/j.nuclphysb.2022.115854
[10] Y. Zhang, Y. Zhu, L. Modesto and C. Bambi, ”Can static regular black holes form from gravitational collapse?”, Eur. Phys. J. C 75, 96 (2015). DOI: https://doi.org/10.1140/epjc/s10052-015-3311-2
[11] A. Borde, ”Open and closed universes, initial singularities and inflation”, Phys. Rev. D 50, 3692 (1994). DOI: https://doi.org/10.1103/PhysRevD.50.3692
[12] A. Borde, ”Regular black holes and topology change”, Phys. Rev. D 55, 7615 (1997). DOI: https://doi.org/10.1103/PhysRevD.55.7615
[13] S. Ansoldi, ”Spherical black holes with regular center: A Review of existing models including a recent realization with Gaussian sources”, DOI: https://doi.org/10.48550/arXiv.0802.0330 [arXiv:0802.0330 [gr-qc]].
[14] J. P. S. Lemos and V.T. Zanchin, ”Regular black holes: Electrically charged solutions, Reissner-Nordstróm outside a de Sitter core”,Phys. Rev. D 83, 124005 (2011). DOI: https://doi.org/10.1103/PhysRevD.83.124005
[15] O.B. Zaslavskii, ”Regular black holes with flux tube core”,Phys. Rev. D 80, 064034 (2009). DOI: https://doi.org/10.1103/PhysRevD.80.064034
[16] A. Kumar, D. V. Singh, Y. Myrzakulov, G. Yergaliyeva and S. Upadhyay, ”Exact solution of Bardeen black hole in Einstein–Gauss–Bonnet gravity”, Eur. Phys. J. Plus 138 (2023) no.12, 1071. DOI: https://doi.org/10.1140/epjp/s13360-023-04718-3
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[20] P. Paul, S. Upadhyay and D. V. Singh,”Charged AdS black holes in 4D Einstein– Gauss–Bonnet massive gravity”, Eur. Phys. J. Plus 138(6), 566 (2023). DOI: https://doi.org/10.1140/epjp/s13360-023-04176-x
[21] B. Singh, B. K. Singh and D. V. Singh, ”Thermodynamics, phase structure of Bardeen massive black hole in Gauss-Bonnet gravity”, Int. J. Geom. Meth. Mod. Phys. 20(08), 2350125 (2023). DOI: 10.1142/S0219887823501256
[22] Y. Myrzakulov, K. Myrzakulov, S. Upadhyay and D. V. Singh, ”Quasinormal modes and phase structure of regular AdS Einstein–Gauss–Bonnet black holes”, Int. J. Geom. Meth. Mod. Phys. 20(07), 2350121 (2023). DOI: https://doi.org/10.1142/S0219887823501219 [arXiv:2305.11201 [gr-qc]]
[23] D. V. Singh, V. K. Bhardwaj and S. Upadhyay, ”Thermodynamic properties, thermal image and phase transition of Einstein-Gauss-Bonnet black hole coupled with nonlinear electrodynamics”, Eur. Phys. J. Plus 137(8), 969 (2022). DOI: https://doi.org/10.1140/epjp/s13360-022-03208-2
[24] C. S. Varsha, V. Venkatesha, N. S. Kavya and D. V. Singh, ”Impact of EUP correction on thermodynamics of AdS black hole”, Annals Phys. 477, 170002 (2025). DOI: https://doi.org/10.1016/j.aop.2025.170002
[25] B. Pourhassan, M. Dehghani, S. Upadhyay, I. Sakalli and D. V. Singh, ”Exponential corrected thermodynamics of Born–Infeld BTZ black holes in massive gravity”, Mod. Phys. Lett. A 37(33,34), 2250230 (2022). DOI: https://doi.org/10.1142/S0217732322502303
[26] A. Kumar, D. V. Singh and S. Upadhyay, ”Impact of Perfect Fluid Dark Matter on the Thermodynamics of AdS Ayón-Beato-GarcÍa Black Holes”, JHAP 4(4), 85 (2024). DOI: 10.22128/jhap.2024.884.1096.
[27] D. V. Singh, S. Upadhyay, Y. Myrzakulov, K. Myrzakulov, B. Singh and M. Kumar, ”Thermodynamic behavior and phase transitions of black holes with a cloud of strings and perfect fluid dark matter”, Nucl. Phys. B 1016, 116915 (2025). DOI: https://doi.org/10.1016/j.nuclphysb.2025.116915
[28] S. G. Ghosh,”A nonsingular rotating black hole”, Eur. Phys. J. C 75(11), 532 (2015). DOI: https://doi.org/10.48550/arXiv.1408.5668 [arXiv:1408.5668 [gr-qc]]
[29] B. K. Vishvakarma, D. V. Singh and S. Siwach, ”Parameter estimation of the BardeenKerr black hole in cloud of strings using shadow analysis”, Phys. Scripta 99 (2024) no.2, 025022. DOI: https://doi.org/10.48550/arXiv.2310.20393 [arXiv:2310.20393 [gr-qc]]
[30] B. K. Vishvakarma, D. V. Singh and S. Siwach, ”Shadows and quasinormal modes of the Bardeen black hole in cloud of strings”, Eur. Phys. J. Plus 138(6), 536 (2023). DOI: https://doi.org/10.1140/epjp/s13360-023-04174-z
[31] R. V. Maluf and J. C. S. Neves,”Thermodynamics of a class of regular black holes with a generalized uncertainty principle”, Phys. Rev. D 97, 104015 (2018). DOI: https://doi.org/10.1103/PhysRevD.97.104015
[32] Mang-Sen Ma and Ren Zhao, ”Corrected form of the first law of thermodynamics for regular black holes”, Class. Quantun Grav. 31, 245014 (2014). DOI: 10.1088/0264- 9381/31/24/245014
[33] A. Kumar, D. V. Singh and S. Upadhyay, ”Ayón–Beato–García black hole coupled with a cloud of strings: Thermodynamics, shadows and quasinormal modes”, Int. J. Mod. Phys. A 39(31), 2450136 (2024). DOI: https://doi.org/10.1142/S0217751X24501367
[34] H. K. Sudhanshu, D. V. Singh, S. Upadhyay, Y. Myrzakulov and K. Myrzakulov, ”Thermodynamics of a newly constructed black hole coupled with nonlinear electrodynamics and cloud of strings”, Phys. Dark Univ. 46, 101648 (2024). DOI: https://doi.org/10.1016/j.dark.2024.101648
[35] B. Singh, D. Veer Singh and B. Kumar Singh, ”Thermodynamics, phase structure and quasinormal modes for AdS Heyward massive black hole”, Phys. Scripta 99(2), 025305 (2024). DOI: 10.1088/1402-4896/ad1da4
[36] P. Paul, S. Upadhyay, Y. Myrzakulov, D. V. Singh and K. Myrzakulov, ”More exact thermodynamics of nonlinear charged AdS black holes in 4D critical gravity”, Nucl. Phys. B 993, 116259 (2023). DOI: https://doi.org/10.1016/j.nuclphysb.2023.116259
[37] D. V. Singh, A. Shukla and S. Upadhyay, ”Quasinormal modes, shadow and thermodynamics of black holes coupled with nonlinear electrodynamics and cloud of strings”, Annals Phys. 447, 169157 (2022). DOI: https://doi.org/10.1016/j.aop.2022.169157
[38] D. V. Singh and S. Siwach, “Thermodynamics and P-v criticality of Bardeen-AdS Black Hole in 4D Einstein-Gauss-Bonnet Gravity,” Phys. Lett. B 808, 135658 (2020). DOI: 10.1016/j.physletb.2020.135658
[39] S. Upadhyay, B. Pourhassan and H. Farahani, ”P-V criticality of first-order entropy corrected AdS black holes in massive gravity”, Phys. Rev. D 95(10), 106014 (2017). DOI: https://doi.org/10.1103/PhysRevD.95.106014
[40] S. H. Hendi, S. Panahiyan, S. Upadhyay and B. Eslam Panah, ”Charged BTZ black holes in the context of massive gravity’s rainbow”, Phys. Rev. D 95(8), 084036 (2017). DOI: https://doi.org/10.1103/PhysRevD.95.084036
[41] V. K. Srivastava, S. Upadhyay, A. K. Verma, D. V. Singh, Y. Myrzakulov and K. Myrzakulov, ”Exploring non-perturbative effects on quasi-topological black hole thermodynamics”, Phys. Dark Univ. 48, 101915 (2025). DOI: https://doi.org/10.1016/j.dark.2025.101915
[42] S. Soroushfar, H. Farahani and S. Upadhyay, ”Non-perturbative correction to thermodynamics of conformally dressed 3D black hole”, Phys. Dark Univ. 42, 101272 (2023). DOI: https://doi.org/10.1016/j.dark.2023.101272 [ arXiv:2404.10309 [gr-qc]]
[43] S. Upadhyay and D. V. Singh, ”Black hole solution and thermal properties in 4D AdS Gauss–Bonnet massive gravity”, Eur. Phys. J. Plus 137(3), 383 (2022). DOI: https://doi.org/10.1140/epjp/s13360-022-02569-y
[44] B. Pourhassan and S. Upadhyay, ”Perturbed thermodynamics of charged black hole solution in Rastall theory”,Eur. Phys. J. Plus 136(3), 311 (2021). DOI: https://doi.org/10.1140/epjp/s13360-021-01271-9
[45] S. Upadhyay, ”Leading-order corrections to charged rotating AdS black holes thermodynamics”,Gen. Rel. Grav. 50(10), 128 (2018). DOI: https://doi.org/10.1007/s10714- 018-2459-0
[46] S. Upadhyay, ”Quantum corrections to thermodynamics of quasitopological black holes”, Phys. Lett. B 775, 130 (2017). DOI: https://doi.org/10.1016/j.physletb.2017.10.059
[47] P. S. Letelier, ”String cosmologies”, Phys. Rev. D 28, 2414 (1983). DOI: https://doi.org/10.1103/PhysRevD.28.2414
[48] P. S. Letelier, ”Fluids of strings in general relativity”, Il Nuovo Cim. B 63, 519 (1981). DOI: https://doi.org/10.1007/BF02755096
[49] P.S. Letelier, ”Clouds of strings in general relativity”, Phys. Rev. D 20, 1294 (1979). DOI: https://doi.org/10.1103/PhysRevD.20.1294
[50] D. V. Singh, S. G. Ghosh and S. D. Maharaj,”Clouds of strings in EinsteinGauss-Bonnet black holes”, Phys. Dark Univ. 30, 100730 (2020). DOI: https://doi.org/10.48550/arXiv.2003.14136 [arXiv:2003.14136 [gr-qc]]
[51] J. D. Bekenstein, ”Black holes and the second law”, Lett. Nuovo Cim. 4, 737 (1972). DOI: https://doi.org/10.1007/BF02757029
[52] J. D. Bekenstein, ”Black holes and entropy”, Phys. Rev. D 7, 2333 (1973). DOI: https://doi.org/10.1103/PhysRevD.7.2333
[53] S. W. Hawking, ”Black holes and thermodynamics”, Phys. Rev. D 13, 191 (1976).DOI: https://doi.org/10.1103/PhysRevD.13.191
[54] M. H. Dehghani and S. H. Hendi, ”Thermodynamics of Rotating Black Branes in Gauss-Bonnet-Born-Infeld Gravity”, Int. J. Mod. Phys. D 16, 1829 (2007). DOI: https://doi.org/10.1142/S0218271807011127
[55] S. G. Ghosh, U. Papnoi, and S. D. Maharaj, ”Cloud of strings in third order Lovelock gravity”, Phys. Rev. D 90, 044068 (2014). DOI: https://doi.org/10.1103/PhysRevD.90.044068
[56] M. Barriola, A. Vilenkin, ”Gravitational field of a global monopole”, Phys. Rev. Lett. 63, 341 (1989). DOI: https://doi.org/10.1103/PhysRevLett.63.341
[2] E.B. Gliner, ”Algebraic Properties of the Energy-momentum Tensor and Vacuum-like States o+ Matter” Sov. Phys. JETP, 22, 378 (1966).
[3] J. Bardeen, ”Non-singular general relativistic gravitational collapse” in Proceedings of GR5 (Tiflis, U.S.S.R., 1968).
[4] E. Ayon-Beato, A. Garcia,”The Bardeen Model as a Nonlinear Magnetic Monopole”, Phys. Lett. B 493, 149 (2000) DOI: https://doi.org/10.1016/S0370-2693(00)01125-4
[5] E. Ayon-Beato and A. Garcia, ”Non-Singular Charged Black Hole Solution for Non-Linear Source”,Gen. Relativ. Gravit. 31, 629 (1999). DOI: https://doi.org/10.1023/A:1026640911319
[6] E. Ayon-Beato and A. Garcia, ”Four Parametric Regular Black Hole Solution”, Gen. Relativ. Gravit.37, 635(2005). DOI: https://doi.org/10.1007/s10714-005-0050-y
[7] E. Ayon-Beato and A. Garcia, ”Regular black hole in general relativity coupled to nonlinear electrodynamics”, Phys. Rev. Lett. 80, 5056 (1998). DOI: https://doi.org/10.1103/PhysRevLett.80.5056
[8] R. G. Daghigh and M. D. Green, ”Gravitational and electromagnetic radiation from an electrically charged black hole in general nonlinear electrodynamics” Phys. Rev. D 105, 024055 (2022). DOI: https://doi.org/10.1103/PhysRevD.105.024055
[9] D. V. Singh, S. G. Ghosh and S. D. Maharaj, ”Exact nonsingular black holes and thermodynamics”, Nucl. Phys. B 981 (2022), 115854. DOI: 10.1016/j.nuclphysb.2022.115854
[10] Y. Zhang, Y. Zhu, L. Modesto and C. Bambi, ”Can static regular black holes form from gravitational collapse?”, Eur. Phys. J. C 75, 96 (2015). DOI: https://doi.org/10.1140/epjc/s10052-015-3311-2
[11] A. Borde, ”Open and closed universes, initial singularities and inflation”, Phys. Rev. D 50, 3692 (1994). DOI: https://doi.org/10.1103/PhysRevD.50.3692
[12] A. Borde, ”Regular black holes and topology change”, Phys. Rev. D 55, 7615 (1997). DOI: https://doi.org/10.1103/PhysRevD.55.7615
[13] S. Ansoldi, ”Spherical black holes with regular center: A Review of existing models including a recent realization with Gaussian sources”, DOI: https://doi.org/10.48550/arXiv.0802.0330 [arXiv:0802.0330 [gr-qc]].
[14] J. P. S. Lemos and V.T. Zanchin, ”Regular black holes: Electrically charged solutions, Reissner-Nordstróm outside a de Sitter core”,Phys. Rev. D 83, 124005 (2011). DOI: https://doi.org/10.1103/PhysRevD.83.124005
[15] O.B. Zaslavskii, ”Regular black holes with flux tube core”,Phys. Rev. D 80, 064034 (2009). DOI: https://doi.org/10.1103/PhysRevD.80.064034
[16] A. Kumar, D. V. Singh, Y. Myrzakulov, G. Yergaliyeva and S. Upadhyay, ”Exact solution of Bardeen black hole in Einstein–Gauss–Bonnet gravity”, Eur. Phys. J. Plus 138 (2023) no.12, 1071. DOI: https://doi.org/10.1140/epjp/s13360-023-04718-3
[17] L. Xiang, Y. Ling and Y. G. Shen, ”Singularities and the Finale of Black Hole Evaporation”, Int. J. Mod. Phys. D 22, 1342016 (2013). DOI: https://doi.org/10.1142/S0218271813420169
[18] H. Culetu, ”On a Regular Charged black Hole with a Nonlinear Electric Source”, Int. J. Theor. Phys. 54, 2855 (2015). DOI: https://doi.org/10.1007/s10773-015-2521-6
[19] L. Balart and E. C. Vagenas, ”Regular black hole metrics and the weak energy condition”, Phys. Lett. B 730, 14 (2014). DOI: https://doi.org/10.1016/j.physletb.2014.01.024
[20] P. Paul, S. Upadhyay and D. V. Singh,”Charged AdS black holes in 4D Einstein– Gauss–Bonnet massive gravity”, Eur. Phys. J. Plus 138(6), 566 (2023). DOI: https://doi.org/10.1140/epjp/s13360-023-04176-x
[21] B. Singh, B. K. Singh and D. V. Singh, ”Thermodynamics, phase structure of Bardeen massive black hole in Gauss-Bonnet gravity”, Int. J. Geom. Meth. Mod. Phys. 20(08), 2350125 (2023). DOI: 10.1142/S0219887823501256
[22] Y. Myrzakulov, K. Myrzakulov, S. Upadhyay and D. V. Singh, ”Quasinormal modes and phase structure of regular AdS Einstein–Gauss–Bonnet black holes”, Int. J. Geom. Meth. Mod. Phys. 20(07), 2350121 (2023). DOI: https://doi.org/10.1142/S0219887823501219 [arXiv:2305.11201 [gr-qc]]
[23] D. V. Singh, V. K. Bhardwaj and S. Upadhyay, ”Thermodynamic properties, thermal image and phase transition of Einstein-Gauss-Bonnet black hole coupled with nonlinear electrodynamics”, Eur. Phys. J. Plus 137(8), 969 (2022). DOI: https://doi.org/10.1140/epjp/s13360-022-03208-2
[24] C. S. Varsha, V. Venkatesha, N. S. Kavya and D. V. Singh, ”Impact of EUP correction on thermodynamics of AdS black hole”, Annals Phys. 477, 170002 (2025). DOI: https://doi.org/10.1016/j.aop.2025.170002
[25] B. Pourhassan, M. Dehghani, S. Upadhyay, I. Sakalli and D. V. Singh, ”Exponential corrected thermodynamics of Born–Infeld BTZ black holes in massive gravity”, Mod. Phys. Lett. A 37(33,34), 2250230 (2022). DOI: https://doi.org/10.1142/S0217732322502303
[26] A. Kumar, D. V. Singh and S. Upadhyay, ”Impact of Perfect Fluid Dark Matter on the Thermodynamics of AdS Ayón-Beato-GarcÍa Black Holes”, JHAP 4(4), 85 (2024). DOI: 10.22128/jhap.2024.884.1096.
[27] D. V. Singh, S. Upadhyay, Y. Myrzakulov, K. Myrzakulov, B. Singh and M. Kumar, ”Thermodynamic behavior and phase transitions of black holes with a cloud of strings and perfect fluid dark matter”, Nucl. Phys. B 1016, 116915 (2025). DOI: https://doi.org/10.1016/j.nuclphysb.2025.116915
[28] S. G. Ghosh,”A nonsingular rotating black hole”, Eur. Phys. J. C 75(11), 532 (2015). DOI: https://doi.org/10.48550/arXiv.1408.5668 [arXiv:1408.5668 [gr-qc]]
[29] B. K. Vishvakarma, D. V. Singh and S. Siwach, ”Parameter estimation of the BardeenKerr black hole in cloud of strings using shadow analysis”, Phys. Scripta 99 (2024) no.2, 025022. DOI: https://doi.org/10.48550/arXiv.2310.20393 [arXiv:2310.20393 [gr-qc]]
[30] B. K. Vishvakarma, D. V. Singh and S. Siwach, ”Shadows and quasinormal modes of the Bardeen black hole in cloud of strings”, Eur. Phys. J. Plus 138(6), 536 (2023). DOI: https://doi.org/10.1140/epjp/s13360-023-04174-z
[31] R. V. Maluf and J. C. S. Neves,”Thermodynamics of a class of regular black holes with a generalized uncertainty principle”, Phys. Rev. D 97, 104015 (2018). DOI: https://doi.org/10.1103/PhysRevD.97.104015
[32] Mang-Sen Ma and Ren Zhao, ”Corrected form of the first law of thermodynamics for regular black holes”, Class. Quantun Grav. 31, 245014 (2014). DOI: 10.1088/0264- 9381/31/24/245014
[33] A. Kumar, D. V. Singh and S. Upadhyay, ”Ayón–Beato–García black hole coupled with a cloud of strings: Thermodynamics, shadows and quasinormal modes”, Int. J. Mod. Phys. A 39(31), 2450136 (2024). DOI: https://doi.org/10.1142/S0217751X24501367
[34] H. K. Sudhanshu, D. V. Singh, S. Upadhyay, Y. Myrzakulov and K. Myrzakulov, ”Thermodynamics of a newly constructed black hole coupled with nonlinear electrodynamics and cloud of strings”, Phys. Dark Univ. 46, 101648 (2024). DOI: https://doi.org/10.1016/j.dark.2024.101648
[35] B. Singh, D. Veer Singh and B. Kumar Singh, ”Thermodynamics, phase structure and quasinormal modes for AdS Heyward massive black hole”, Phys. Scripta 99(2), 025305 (2024). DOI: 10.1088/1402-4896/ad1da4
[36] P. Paul, S. Upadhyay, Y. Myrzakulov, D. V. Singh and K. Myrzakulov, ”More exact thermodynamics of nonlinear charged AdS black holes in 4D critical gravity”, Nucl. Phys. B 993, 116259 (2023). DOI: https://doi.org/10.1016/j.nuclphysb.2023.116259
[37] D. V. Singh, A. Shukla and S. Upadhyay, ”Quasinormal modes, shadow and thermodynamics of black holes coupled with nonlinear electrodynamics and cloud of strings”, Annals Phys. 447, 169157 (2022). DOI: https://doi.org/10.1016/j.aop.2022.169157
[38] D. V. Singh and S. Siwach, “Thermodynamics and P-v criticality of Bardeen-AdS Black Hole in 4D Einstein-Gauss-Bonnet Gravity,” Phys. Lett. B 808, 135658 (2020). DOI: 10.1016/j.physletb.2020.135658
[39] S. Upadhyay, B. Pourhassan and H. Farahani, ”P-V criticality of first-order entropy corrected AdS black holes in massive gravity”, Phys. Rev. D 95(10), 106014 (2017). DOI: https://doi.org/10.1103/PhysRevD.95.106014
[40] S. H. Hendi, S. Panahiyan, S. Upadhyay and B. Eslam Panah, ”Charged BTZ black holes in the context of massive gravity’s rainbow”, Phys. Rev. D 95(8), 084036 (2017). DOI: https://doi.org/10.1103/PhysRevD.95.084036
[41] V. K. Srivastava, S. Upadhyay, A. K. Verma, D. V. Singh, Y. Myrzakulov and K. Myrzakulov, ”Exploring non-perturbative effects on quasi-topological black hole thermodynamics”, Phys. Dark Univ. 48, 101915 (2025). DOI: https://doi.org/10.1016/j.dark.2025.101915
[42] S. Soroushfar, H. Farahani and S. Upadhyay, ”Non-perturbative correction to thermodynamics of conformally dressed 3D black hole”, Phys. Dark Univ. 42, 101272 (2023). DOI: https://doi.org/10.1016/j.dark.2023.101272 [ arXiv:2404.10309 [gr-qc]]
[43] S. Upadhyay and D. V. Singh, ”Black hole solution and thermal properties in 4D AdS Gauss–Bonnet massive gravity”, Eur. Phys. J. Plus 137(3), 383 (2022). DOI: https://doi.org/10.1140/epjp/s13360-022-02569-y
[44] B. Pourhassan and S. Upadhyay, ”Perturbed thermodynamics of charged black hole solution in Rastall theory”,Eur. Phys. J. Plus 136(3), 311 (2021). DOI: https://doi.org/10.1140/epjp/s13360-021-01271-9
[45] S. Upadhyay, ”Leading-order corrections to charged rotating AdS black holes thermodynamics”,Gen. Rel. Grav. 50(10), 128 (2018). DOI: https://doi.org/10.1007/s10714- 018-2459-0
[46] S. Upadhyay, ”Quantum corrections to thermodynamics of quasitopological black holes”, Phys. Lett. B 775, 130 (2017). DOI: https://doi.org/10.1016/j.physletb.2017.10.059
[47] P. S. Letelier, ”String cosmologies”, Phys. Rev. D 28, 2414 (1983). DOI: https://doi.org/10.1103/PhysRevD.28.2414
[48] P. S. Letelier, ”Fluids of strings in general relativity”, Il Nuovo Cim. B 63, 519 (1981). DOI: https://doi.org/10.1007/BF02755096
[49] P.S. Letelier, ”Clouds of strings in general relativity”, Phys. Rev. D 20, 1294 (1979). DOI: https://doi.org/10.1103/PhysRevD.20.1294
[50] D. V. Singh, S. G. Ghosh and S. D. Maharaj,”Clouds of strings in EinsteinGauss-Bonnet black holes”, Phys. Dark Univ. 30, 100730 (2020). DOI: https://doi.org/10.48550/arXiv.2003.14136 [arXiv:2003.14136 [gr-qc]]
[51] J. D. Bekenstein, ”Black holes and the second law”, Lett. Nuovo Cim. 4, 737 (1972). DOI: https://doi.org/10.1007/BF02757029
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Volume 6, Issue 4
May 2026Pages 171-184
- Receive Date: 16 November 2025
- Revise Date: 15 December 2025
- Accept Date: 29 December 2025