Heat capacities and thermodynamic geometry in deformed Jackiw–Teitelboim gravity

In this paper, we will study some thermodynamic features and phase structure of charged AdS black holes in deformed Jackiw–Teitelboim (dJT) gravity. We find the values of temperature, entropy and electric charge at the critical inflection points of the corresponding solutions. In addition, we compute the heat capacity as thermal stability parameter along with the expansion coefficient and isothermal compressibility as thermodynamic response functions in dJT model. It is shown that they are divergent at the critical points of the isocharge curves and satisfy the Ehrenfest’s equations which discloses this fact that the phase transition at the critical points is of second order. In the context of thermodynamic geometry, we also compute the state scalar curvature, R, of these black holes following three practical methods; Weinhold, Ruppeiner and New thermodynamic geometry. This provides more insights into the behavior and significance of the scalar curvature near the critical points of charged AdS black holes in dJT theory, analogous to that for conventional critical phenomena.