Eur. Phys. J. Plus (2021) 136: 284
https://doi.org/10.1140/epjp/s13360-021-01270-w

Regular Article

$P-V$ criticality and phase transition of the Kerr-Sen-AdS Black Hole

Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, 54590, Lahore, Pakistan

^a msharif.math@pu.edu.pk

Received: 22 October 2020
Accepted: 23 February 2021
Published online: 3 March 2021

Abstract

In this paper, we analyze the critical phenomena and phase transition of the Kerr-Sen-anti-de Sitter black hole in the framework of Maxwell equal-area law. First, we review the exact expressions of thermodynamic quantities such as entropy, Hawking temperature and angular momentum in the extended phase space. These quantities satisfy the usual first law of thermodynamics as well as Smarr–Gibbs–Dehum relation. The critical behavior of thermodynamic quantities is analyzed through two techniques, i.e., Maxwell equal-area law and van der Waal-like equation of state. It is found that the former technique is more proficient to study the critical behavior of complicated black holes. Second, we construct phase diagram in $T-S$ conjugate variables and find an isobar using equal-area law. It is concluded that below the critical pressure, black holes observe similar phase transition as that of liquid-gas van der Waal fluid. Finally, we analyze the impact of thermal fluctuations on the stability of considered black hole solution.