Black hole thermodynamics in ( $$2+1$$ 2 + 1 )-dimensional scalar–tensor-Born–Infeld theory - M. Dehghani (European Physical Journal C: Particles and Fields, 2022)
Abstract The action of scalar–tensor (ST) gravity theory can be written in both of the Jordan and Einstein frames, which are related via conformal transformations. Here, by introducing a suitable conformal transformation (CT), the action of three-dimensional Einstein-dilaton-Born–Infeld (EdBI) gravity has been obtained from that of scalar–tensor-Born–Infeld (STBI) theory. Despite the field equations of ST gravity, the exact solutions of Einstein-dilaton (Ed) theory can be obtained, easily. The exact solutions of STBI theory have been obtained from those of EdBI gravity by applying the inverse CTs. As the result, two novel classes of ST black hole (BH) solutions have been introduced in the presence of Born–Infeld (BI) nonlinear electrodynamics. The BHs’ conserved and thermodynamic quantities have been calculated under the influence of nonlinear electrodynamics. Then, through a Smarr-type mass formula, it has been shown that these quantities satisfy the standard form of the thermodynamical first law, in both of the Jordan and Einstein frames. Thermal stability or phase transition of the BHs have been investigate by use of the canonical ensemble method and regarding the signature of specific heat (SH). The points of first- and second-order phase transitions, and the size of those BHs which remain locally stable have been determined.