Journal of Holography Applications in Physics
GUP-Deformed Thermodynamic Behavior of Cylindrical Black Strings in Four Dimensions
Document Type : Regular article
Authors
Department of Physics, NIT Srinagar, Jammu and Kashmir, India
Abstract
We investigate the thermodynamic properties of four-dimensional cylindrically symmetric black strings embedded in an Anti-de Sitter (AdS) spacetime. By incorporating the Generalized Uncertainty Principle (GUP), we introduce minimal length corrections to the thermodynamic framework, thereby capturing quantum gravity effects in the near-horizon regime. We demonstrate that these GUP-induced modifications lead to logarithmic corrections in the entropy-area relation, particularly for small horizon radii, while preserving thermodynamic consistency with the first law of thermodynamics. Through a detailed analysis of the Helmholtz and Gibbs free energies, we observe that the equation of state is significantly deformed by quantum corrections, driving instabilities in black strings with sufficiently small horizon radii. The study of specific heat capacity further confirms a phase transition from stable to unstable configurations, highlighting the role of the minimal length scale on the thermal stability of black string systems.
Keywords
Main Subjects
Article PDF
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[2] J. M. Bardeen, B. Carter and S. W. Hawking, “The four laws of black hole mechanics,” Commun. Math. Phys. 31, 161 (1973). DOI: 10.1007/BF01645742.
[3] J. D. Bekenstein, “Black holes and the second law,” 303 (2020). DOI: 10.1142/9789811203961_0022.
[4] J. D. Bekenstein, “Generalized second law of thermodynamics in black-hole physics,” Phys. Rev. D 9, 3292 (1974). DOI: 10.1103/PhysRevD.9.3292.
[5] S. Das, P. Majumdar and R. K. Bhaduri, “General logarithmic corrections to black-hole entropy,” Class. Quantum Grav. 19, 2355 (2002). DOI: 10.1088/0264-9381/19/9/302.
[6] A. Ghosh and P. Mitra, “Understanding the area proposal for extremal black hole entropy,” Phys. Rev. Lett. 78, 1858 (1997). DOI: 10.1103/PhysRevLett.78.1858.
[7] S. Upadhyay and P. A. Ganai, “A modified thermodynamics of rotating and charged BTZ black hole,” arXiv:1912.00767 (2019). DOI: https://arxiv.org/abs/1912.00767.
[8] P. A. Ganai and S. Upadhyay, “Thermal fluctuations to the thermodynamics of a non-rotating BTZ black hole,” Prog. Theor. Exp. Phys. 2019, 103B06 (2019). DOI: 10.1093/ptep/ptz113.
[9] P. A. Ganai, “Implications of quantum corrections on the thermodynamics of charged AdS black hole,” J. Hologr. Appl. Phys. 3, 23 (2023). DOI:10.22128/jhap.2023.664.1045.
[10] N. Islam and P. A. Ganai, “Quantum corrections to thermodynamics of BTZ black hole,” Int. J. Mod. Phys. A 34, 1950063 (2019). DOI: 10.1142/S0217751X19500635.
[11] N. Islam and P. A. Ganai, “Quantum corrections to AdS black hole in massive gravity,” Int. J. Mod. Phys. A 34, 1950225 (2019). DOI: 10.1142/S0217751X19502257.
[12] N. Islam and P. A. Ganai, “First-order corrected thermodynamic potentials characterizing BTZ black hole in massive gravity,” Int. J. Mod. Phys. A 35, 2050080 (2020). DOI: 10.1142/S0217751X20500803.
[13] W. A. Dar, N. U. I. Rather and P. A. Ganai, “Redefining thermodynamic potentials in 2+1 dimensional massive gravity,” J. Hologr. Appl. Phys. 5, 31 (2025). DOI: 10.22128/jhap.2024.900.1099.
[14] N. Islam, K. Z. Amin and P. A. Ganai, “Thermodynamic response of a perturbed BTZ black hole,” Int. J. Geom. Methods Mod. Phys. 2550244 (2025). DOI: 10.1142/S0219887825502445.
[15] K. Z. Amin et al., “Thermodynamic implications of perturbed entropy in 5D black holes,” Int. J. Mod. Phys. A 40, 2550057 (2025). DOI: 10.1142/S0217751X25500575.
[16] K. Z. Amin and P. A. Ganai, “Dynamics of a perturbed higher dimensional black hole,” Int. J. Theor. Phys. 63, 208 (2024). DOI: 10.1007/s10773-024-05750-4.
[17] K. Z. Amin et al., “Electrostatic implications of exponential corrections,” Int. J. Geom. Methods Mod. Phys. 2550219 (2025). DOI: 10.1142/S0219887825502196.
[18] A. Ashtekar and M. Bojowald, “Black hole evaporation: A paradigm,” Class. Quantum Grav. 22, 3349 (2005). DOI: 10.1088/0264-9381/22/16/014.
[19] H. Saida, “Black hole evaporation and nonequilibrium thermodynamics,” arXiv:grqc/0505089 (2005). DOI: 10.48550/arXiv.gr-qc/0505089.
[20] A. Ghosh and P. Mitra, “Ghosh and Mitra reply,” Phys. Rev. Lett. 80, 3413 (1998). DOI: 10.1103/PhysRevLett.80.3413.
[21] D. Birmingham and S. Sen, “Exact black hole entropy bound,” Phys. Rev. D 63, 047501 (2001). DOI: 10.1103/PhysRevD.63.047501.
[22] B. Pourhassan et al., “Quantum gravity effects on Hořava–Lifshitz black hole,” Nucl. Phys. B 928, 415 (2018). DOI: 10.1016/j.nuclphysb.2018.01.018.
[23] S. Upadhyay, “Leading-order corrections to charged rotating AdS black holes,” Gen. Relativ. Gravit. 50, 128 (2018). DOI: 10.1007/s10714-018-2459-0.
[24] G. T. Horowitz and K. Maeda, “Fate of the black string instability,” Phys. Rev. Lett. 87, 131301 (2001). DOI: 10.1103/PhysRevLett.87.131301.
[25] Y. Brihaye, E. Radu and C. Stelea, “Black strings with a negative cosmological constant,” Class. Quantum Grav. 24, 4839 (2007). DOI: 10.1088/0264-9381/24/18/017.
[26] R.-G. Cai and Y.-Z. Zhang, “Black plane solutions,” Phys. Rev. D 54, 4891 (1996). DOI: 10.1103/PhysRevD.54.4891.
[27] G. W. Gibbons and S. W. Hawking, “Action integrals and partition functions,” Phys. Rev. D 15, 2752 (1977). DOI: 10.1103/PhysRevD.15.2752.
[28] H. W. Braden et al., “Charged black hole in a grand canonical ensemble,” Phys. Rev. D 42, 3376 (1990). DOI: 10.1103/PhysRevD.42.3376.
[29] S. H. Hendi et al., “Black string in massive gravity,” Nucl. Phys. B 965, 115362 (2021). DOI: 10.1016/j.nuclphysb.2021.115362.
[30] S. G. Ghosh et al., “Rotating black strings,” Phys. Rev. D 101, 104042 (2020). DOI: 10.1103/PhysRevD.101.104042.
[31] D. V. Ahluwalia, “Interface of gravitational and quantum realms,” Mod. Phys. Lett. A 17, 1135 (2002). DOI: 10.1142/S021773230200765X.
[32] S. Hossenfelder, “Minimal length scale scenarios,” Living Rev. Relativ. 16, 2 (2013). DOI: 10.12942/lrr-2013-2.
[33] H. S. Snyder, “Quantized space-time,” Phys. Rev. 71, 38 (1947). DOI: 10.1103/PhysRev.71.38.
[34] A. Connes, J. Cuntz and M. A. Rieffel, “Noncommutative geometry,” Oberwolfach Rep. 6, 2271 (2010). DOI: 10.4171/OWR/2007/43.
[35] A. Kempf, G. Mangano and R. B. Mann, “Hilbert space representation,” Phys. Rev. D 52, 1108 (1995). DOI: 10.1103/PhysRevD.52.1108.
[36] K. Nouicer, “Casimir effect in minimal length,” J. Phys. A 38, 10027 (2005). DOI: 10.1088/0305-4470/38/46/009.
[37] J. W. Moffat, “Black holes in modified gravity,” Eur. Phys. J. C 75, 175 (2015). DOI: 10.1140/epjc/s10052-015-3405-x.
[38] E. Spallucci, A. Smailagic and P. Nicolini, “Trace anomaly,” Phys. Rev. D 73, 084004 (2006). DOI: 10.1103/PhysRevD.73.084004.
[39] P. Nicolini, A. Smailagic and E. Spallucci, “Noncommutative Schwarzschild black hole,” Phys. Lett. B 632, 547 (2006). DOI: 10.1016/j.physletb.2005.11.004.
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Volume 7, Issue 1
July 2026Pages 64-80
- Receive Date: 02 January 2026
- Revise Date: 23 February 2026
- Accept Date: 23 February 2026