On the Nonlinear Equation of State in Black Hole Thermodynamics

Document Type : Research Article

Author

Department of Physics, K.L.S. College, Nawada, Magadh University, Bodh Gaya, Bihar 805110, India

Abstract

The study of black hole thermodynamics has revealed profound connections between gravitation, quantum theory, and statistical mechanics. In many instances, the key physical information is encoded in nonlinear algebraic or transcendental equations that relate horizon radius, temperature, and pressure. In this work, we examine a specific nonlinear equation arising from the extended phase space of charged anti-de Sitter (AdS) black holes. By analyzing its structure and obtaining approximate and exact solutions, we highlight the physical implications for the thermodynamic stability of black holes. Our results clarify the role of nonlinearities in determining critical points and phase transitions analogous to the van der Waals fluid.

Keywords

Main Subjects

Full Text

 

Article PDF

References

[1] J. D. Bekenstein, Black holes and entropy, Phys. Rev. D 7, 2333–2346, (1973).
[2] S. W. Hawking, Particle creation by black holes, Commun. Math. Phys. 43, 199–220, (1975).
[3] P. C. W. Davies, Thermodynamics of black holes, Rep. Prog. Phys. 41, 1313–1355, (1978).
[4] S. W. Hawking and D. N. Page, Thermodynamics of black holes in anti–de Sitter space, Commun. Math. Phys. 87, 577–588, (1983).
[5] E. Witten, Anti–de Sitter space and holography, Adv. Theor. Math. Phys. 2, 253–291, (1998).
[6] D. Kastor, S. Ray, and J. Traschen, Enthalpy and the mechanics of AdS black holes, Class. Quantum Grav. 26, 195011, (2009).
[7] B. P. Dolan, Pressure and volume in the first law of black hole thermodynamics, Class. Quantum Grav. 28, 235017, (2011).
[8] M. Cvetic, G. Gibbons, D. Kubizˇnák, and C. Pope, Black hole enthalpy and an entropy inequality for the thermodynamic volume, ˇ Phys. Rev. D 84, 024037, (2011).
[9] D. Kubiznák and R. B. Mann, ˇ P–V criticality of charged AdS black holes, JHEP 07, 033, (2012).
[10] N. Altamirano, D. Kubiznák, R. B. Mann, and Z. Sherkatghanad, Kerr-AdS analog of triple point and solid/liquid/gas phase ˇ transition, Class. Quantum Grav. 31, 042001, (2014).
[11] A. M. Frassino, D. Kubiznák, R. B. Mann, and F. Simovic, Multiple reentrant phase transitions and triple points in Lovelock ˇ thermodynamics, JHEP 09, 080, (2014).
[12] R. A. Hennigar and R. B. Mann, Black holes in Einsteinian cubic gravity, Phys. Rev. D 95, 064055, (2017).
[13] A. Karch and B. Robinson, Holographic black hole chemistry, JHEP 12, 073, (2015).
[14] R.-G. Cai, Gauss-Bonnet black holes in AdS spaces, Phys. Rev. D 65, 084014, (2002).
[15] R.-G. Cai, Thermodynamics of conformal anomaly corrected black holes in AdS space, Phys.Lett.B 733, 183–189, (2014).
[16] G. Ruppeiner, Riemannian geometry in thermodynamic fluctuation theory, Rev. Mod. Phys. 67, 605–659, (1995).
[17] G. Ruppeiner, Thermodynamic curvature and phase transitions in Kerr–Newman black holes, Phys. Rev. D 78, 024016, (2008).
[18] S.-W. Wei and Y.-X. Liu, Insight into the microscopic structure of an AdS black hole from thermodynamical phase transition, Phys. Rev. Lett. 115, 111302, (2015). 
Analytical and Numerical Solutions for Nonlinear Equations
Volume 9, Issue 2
September 2025
Pages 270-279

Files

History

  • Receive Date: 16 September 2025
  • Accept Date: 13 October 2025
  • Publish Date: 29 October 2025

Share

How to cite

Statistics