$P-V$ Criticality of Conformal Gravity Holography in Four Dimensions

Abstract

{We examine the critical behaviour 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 {non-trivial} \emph{Rindler parameter ($a$)} in the {spacetime geometry. This geometric parameter has an important role to construct a model for gravity at large distances where the parameter "$a$" actually originates}. We also investigate the effect of the said parameter on the {black hole~(BH) \emph{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-AdS~(anti de-Sitter) BH and {the} chargeless-AdS BH. Interestingly, we find {that} the \emph{critical ratio} for this BH is ${\rho }_c=\frac{P_c{v}_c}{T_c}=\frac{\sqrt{3}}{2}\left(3\sqrt{2}-2\sqrt{3}\right)$, which is greater than the charged AdS BH and Schwarzschild-AdS BH {i.e.} ${\rho }_c^{CG}:{\rho }_c^{Sch-AdS}:{\rho }_c^{RN-AdS}=0.67:0.50:0.37$. The symbols are defined in the main work. Moreover, we observe that \emph{{the} critical ratio {has a constant value}} and {it is} independent of the {non-trivial} \emph{Rindler parameter ($a$)}. Finally, we derive {the} \emph{reduced equation of state} in terms of {the} \emph{reduced temperature}, {the} \emph{reduced volume} and {the} \emph{reduced pressure} respectively.

Accepted in MPLA, Modern Physics Letters A, 2018

References in corpus (5)

• Black Hole Enthalpy and an Entropy Inequality for the Thermodynamic Volume
• Einstein Gravity from Conformal Gravity
• Effects of dark energy on P-V criticality of charged AdS black holes
• Model for gravity at large distances
• Mass Independent Area (or Entropy) and Thermodynamic Volume Products in Conformal Gravity

Cited by in corpus (3)

• Charged AdS black holes in Gauss-Bonnet gravity and nonlinear electrodynamics
• NED-AdS black holes, extended phase space thermodynamics and Joule--Thomson expansion
• AdS black holes in the framework of nonlinear electrodynamics, thermodynamics and Joule--Thomson expansion