Area products for ${\cal H}^{\pm}$ in AdS space

Abstract

We derive the thermodynamic products particularly area (or entropy) products of ${\cal H}^{\pm}$ for certain class of black holes in AdS space. We show by explicit and exact calculations that more complicated function of event horizon area and Cauchy horizon area is indeed mass-independent. This mass-independent quantities indicate that they \emph{could turn out to be an "universal" quantity} provided that they depends only on the quantized angular momentum, quantized charges, and cosmological constant respectively. Furthermore, these area (or entropy) product relations for several class of black holes in AdS space gives us strong indication to understanding the nature of non-extremal black hole entropy (both inner and outer) at the microscopic level. Moreover, we compute the Penrose's famous \emph{Cosmic Censorship Inequality} (which requires Cosmic-Censorship hypothesis) for these class of black holes in AdS space . Local thermodynamic stability has been discussed for these black holes and under certain condition certain black holes displayed second order phase transition.