Extended phase space thermodynamics of Bardeen black hole in massive gravity
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Extended phase space thermodynamics of Bardeen black hole in massive gravity Benoy Kumar Singha , Raj Pal Singhb , Dharm Veer Singhc Department of Physics, Institute of Applied Science and Humanities, GLA University, Mathura 281406, India Received: 14 August 2020 / Accepted: 23 October 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract We present an exact solution of Bardeen Ad S black hole in massive gravity theory by taking into account the massive gravity parameter m and study its thermodynamic properties such as temperature, entropy and heat capacity at constant pressure. We also study the critical behaviour of Bardeen Ad S massive black holes by taking the cosmological constant as the thermodynamic pressure, and it is shown that thermodynamic volume is independent of the massive gravity parameter m. In addition to these, we investigate the dependence of critical parameters on the massive gravity parameter (m) and magnetic monopole charge (e). It is observed that the critical exponents (critical temperature and critical pressure) increase with massive gravity parameter but decrease in the presence of magnetic monopole charge. Also the numerical value of ratio Pc rc /Tc increases with increase in the values of the parameters m and e.
1 Introduction Black holes, coined by Wheeler [1], were generally considered as esoteric objects of purely theoretical interest and of little physical relevance. It is well known that a black hole is a thermodynamical system which shows fundamental connections between the thermodynamics and general relativity since the discovery of black hole entropy by Bekenstein in [2–5] and Hawking [6]. During the past years, the development of Maldacena conjecture (AdS/CFT correspondence) [7] has attracted significant attention to AdS black holes. The investigation of Ad S black holes revealed new features and subsequent studies found that the Ad S black hole behaves like the Van der Waals fluid. The first regular black hole was proposed by Bardeen [8] and later on an exact solution of black hole was given by Ayon-Beato and Garcia [9–11] wherein general relativity coupled with nonlinear electrodynamics. Thereafter, more intense emphasis was given by researchers in investigating the regular black holes solutions [12–21]. But most of these solutions are based on Bardeen’s model [8]. In later years, the generalized solutions of Bardeen black hole model were developed which include Bardeen de Sitter black hole [22,23], rotating Bardeen
a e-mail: [email protected] b e-mail: [email protected] c e-mail: [email protected] (corresponding author)
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solution [24], non-commutative Bardeen solution [25], higher-dimensional black holes [26] and EGB black holes [27–31] etc. However, many black hole solutions with massive gravity [32–35] are already available in the literature, but they are not regular black hole solutions. In the extended phase space, cosmo
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