Thermodynamics of novel scalar–tensor-Born–Infeld black holes

Abstract

Two novel classes of four-dimensional exact black hole (BH) solutions have been obtained in the scalar–tensor (ST) theory which are coupled to Born–Infeld (BI) electrodynamics. To this end, a conformal transformation (CT) has been applied which transforms the action of ST–BI gravity to that of Einstein–dilaton–BI theory. The scalar-coupled BI theory, which has been introduced here, slightly differs from those have been used, previously. The analytical solutions have been obtained in the Einstein frame (EF) and two classes of charged dilatonic BHs, with unusual asymptotic behaviors, have been presented. All the solutions coincide with the corresponding values of Einstein–dilaton–Maxwell theory, in the limit of large BI parameter. By calculating thermodynamic parameters and, noting the Smarr mass relation, we showed that the first law of BH thermodynamics (FLT) is valid for the novel dilatonic BHs. Stability of the BHs has been investigated in EF, making use of the canonical ensemble method and noting the signature of the BH heat capacity (HC). Next, by use of the inverse CT, the solutions of ST theory have been obtained from their EF counterparts. Although, the entropy of ST BHs violates entropy-area law, the thermodynamic and conserved quantities have been obtained noting their conformal invariance property. It has been found that the ST BHs have the same thermodynamic and stability properties as the Einstein–dilaton ones.