P–V criticality of conformal gravity holography in four dimensions

Abstract

We examine the critical behavior, i.e. P–V criticality of conformal gravity (CG) in an extended phase space in which the cosmological constant should be interpreted as a thermodynamic pressure and the corresponding conjugate quantity as a thermodynamic volume. The main potential point of interest in CG is that there exists a nontrivial Rindler parameter [Formula: see text] in the spacetime geometry. This geometric parameter has an important role to construct a model for gravity at large distances where the parameter “[Formula: see text]” actually originates. We also investigate the effect of the said parameter on the black hole (BH) thermodynamic equation of state, critical constants, Reverse Isoperimetric Inequality, first law of thermodynamics, Hawking–Page phase transition and Gibbs free energy for this BH. We speculate that due to the presence of the said parameter, there has been a deformation in the shape of the isotherms in the P–V diagram in comparison with the charged-anti de Sitter (AdS) BH and the chargeless-AdS BH. Interestingly, we find that the critical ratio for this BH is [Formula: see text], which is greater than the charged AdS BH and Schwarzschild–AdS BH, i.e. [Formula: see text]. The symbols are defined in the main work. Moreover, we observe that the critical ratio has a constant value and it is independent of the nontrivial Rindler parameter [Formula: see text]. Finally, we derive the reduced equation of state in terms of the reduced temperature, the reduced volume and the reduced pressure, respectively.