Thermodynamic Product Relations for Generalized Regular Black Hole

We derive thermodynamic product relations for four-parametric regular black hole (BH) solutions of the Einstein equations coupled with a non-linear electrodynamics source. The four parameters can be described by the mass ($m$), charge ($q$), dipole moment ($\alpha$) and quadrupole moment ($\beta$) respectively. We study its complete thermodynamics. We compute different thermodynamic products i.e. area product, BH temperature product, specific heat product and Komar energy product respectively. Furthermore, we show that some complicated function of horizon areas that is indeed \emph{mass-independent} and could turn out to be \emph{universal}.Comment: Version accepted in Advances in High Energy Physic

Thermodynamic Products for Sen Black Hole

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).Comment: Accepted for publication in EPJ