Mass Independent Area (or Entropy) and Thermodynamic Volume Products in Conformal Gravity (1603.07744v2)

Abstract: In this work we investigate the thermodynamic properties of conformal gravity in four dimensions. We compute the \emph{area(or entropy) functional} relation for this black hole. We consider both de-Sitter (dS) and anti de-Sitter (AdS) cases. We derive the \emph{Cosmic-Censorship-Inequality} which is an important relation in general relativity that relates the total mass of a spacetime to the area of all the black hole horizons. Local thermodynamic stability is studied by computing the specific heat. The second order phase transition occurs at a certain condition. Various type of second order phase structure has been given for various values of $a$ and the cosmological constant $\Lambda$ in the Appendix. When $a=0$, one obtains the result of Schwarzschild-dS and Schwarzschild-AdS cases. In the limit $aM<<1$, one obtains the result of Grumiller space-time. Where $a$ is non-trivial Rindler parameter or Rindler acceleration and $M$ is the mass parameter. The \emph{thermodynamic volume functional} relation is derived in the \emph{extended phase space}, where the cosmological constant treated as a thermodynamic pressure and its conjugate variable as a thermodynamic volume. The \emph{mass-independent} area (or entropy) functional relation and thermodynamic volume functional relation that we have derived could turn out to be a \emph{universal} quantity.