Holographic thermodynamics of Kerr–Einstein–Maxwell–dilaton–axion–Anti-de-Sitter black hole

Abstract

This work reports a novel investigation of the bulk and CFT thermodynamics of Kerr–EMDA–AdS black hole in 3+1-dimensional AdS spacetime. We comprehensively present the construction of mass functions, the enthalpy analog, of the black hole for both scenarios and derive thermodynamic quantities from there. In the first part of this work, we derive an analytical expression of the bulk temperature, angular momentum per unit mass, electric field, thermodynamic volume, Gibbs and Helmholtz’s free energy functions, internal energy, specific heat capacities, adiabatic compressibility and the thermodynamic black hole’s speed of sound analog. The critical point of the analog Van der Waals phase transition is also analytically investigated. The second part of this work focuses on the CFT thermodynamics counterpart, especially on the critical phenomena. The behavior of the temperature, Helmholtz’s free energy and the heat capacity are analytically and graphically explored in various thermodynamical aspects. The last part of this work is dedicated to investigate the critical phenomena in F̄−T̄ and Ḡ−T̄ frameworks via implicit method. Interestingly, we also find that the Kerr–EMDA–AdS black hole exhibits not only first-order phase transitions in the dual CFT, but also a reentrant phase transition, characterized by a multibranched structure of the heat capacity.