Thermodynamic geometry of charged rotating black holes in Einsteinian cubic gravity

Abstract

We study the thermodynamic geometry of two types of asymptotically anti-de Sitter black holes in four-dimensional Einsteinian cubic gravity, including the uncharged rotating and charged non-rotating black holes, applying the Ruppeiner thermodynamic geometry method. The divergence of the scalar curvature of the Ruppeiner metric ([Formula: see text]) is found to be related to the vanishing of the heat capacity. The stability of the solutions is shown to be affected by the Einsteinian cubic gravity coupling constant [Formula: see text]. In the unstable phase of the rotating black hole, the [Formula: see text] appeared to possess additional diverging points, where the number of these points and the behavior of [Formula: see text] are controlled by the angular momentum parameter. Also, for the charged non-rotating black hole case, we show that depending on the values of [Formula: see text], the solution may enjoy two types of phase transition and [Formula: see text] behaviors. The characteristic behavior of [Formula: see text] of these two types of black holes enabled us to recognize the types of interactions between microscopic degrees of freedom.