BTZ black hole in [formula omitted] gravity and thermodynamic properties

Abstract

In this study, we aim to investigate the rotating Banados-Teitelboim-Zanelli (BTZ) black hole (BH) solution within the framework of modified gravity theories. Notably, our investigation reveals that the BTZ BH space–time serves as a solution within the framework of Ricci-inverse (RI) gravity, particularly within Class-I models defined by f(R,A)=(R+αA). Here, R=gμνRμν and A=gμνAμν denote the Ricci and anti-curvature scalars, respectively, while α represents the coupling parameter. We show that this new modified theory induces modifications to the cosmological constant, demonstrating the influence of the coupling parameter α when analyzed in a vacuum as matter content. Additionally, we study the thermodynamic properties of this BTZ BH solution obtained within the RI-gravity framework and analyze the associated physical quantities. It is evident that the thermodynamic parameters, including BH horizons, Hawking temperature, entropy, free energy, internal energy, and specific heat capacity, undergo alterations due to the coupling constant α. Specifically, when α=0, our findings align with the outcomes documented in existing literature obtained in the general relativity (GR) context using the BTZ BH solution.