Area Products forH± in AdS Space

We derive the thermodynamic products, in particular the area (or entropy) products ofH± for a wide variety of black holes (BHs) in anti-de Sitter (AdS) space. We show by explicit and exact calculations that, for this class of BHs, more complicated functions of the event horizon area and Cauchy horizon area are indeed mass-independent. This mass-independent results indicate that they could turn out to be a “universal” quantity provided that they depend only on the quantized angular momentum, quantized charges, and cosmological constant, etc. Furthermore, these area (or entropy) product relations for several classes of BHs in AdS space gives us strong indication to understanding the nature of non-extremal BH entropy (both inner and outer) at the microscopic level. Moreover, we compute the famous Cosmic Censorship Inequality (which requires Cosmic-Censorship hypothesis) for these classes of BHs in AdS space. Local thermodynamic stability has been discussed for these BHs and under certain conditions, these classes of BHs displayed second order phase transition. The super-entropic BH does not provide any kind of second order phase transition.