Thermodynamic Products for Sen Black Hole

Abstract

We investigate the properties of inner and outer horizon thermodynamics of Sen black hole(BH) both in \emph{Einstein frame(EF)} and \emph{string frame(SF)}. We also compute area(or entropy) product, area(or entropy) sum of the said BH in EF as well as SF. In the EF, we observe that the area(or entropy) product is \emph{ universal}, whereas area (or entropy) sum is \emph{not} universal. On the other hand, in the SF, area(or entropy) product and area(or entropy) sum don't have any universal behavior because they all are depends on ADM(Arnowitt-Deser-Misner) mass parameter. We also verify that the \emph{first law} is satisfied at the Cauchy horizon(CH) as well as event horizon(EH). In addition, we also compute other thermodynamic products and sums in the EF as well as in the SF. We further compute the \emph{Smarr mass formula} and \emph{Christodoulou's irreducible mass formula} for Sen BH. Moreover, we compute the area bound and entropy bound for both the horizons. The upper area bound for EH is actually the Penrose like inequality, which is the first geometric inequality in BHs. Furthermore, we compute the central charges of the left and right moving sectors of the dual CFT in Sen/CFT correspondence using thermodynamic relations. These thermodynamic relations on the multi-horizons give us further understanding the microscopic nature of BH entropy(both interior and exterior).