Ruppeiner geometry, P–V criticality and interacting microstructures of black holes in dRGT massive gravity

Abstract

We probe the microstructure of the dRGT massive black hole in an anti-de Sitter background. The calculations are performed in an extended phase space with pressure and volume taken as fluctuation variables. We analyze the microstructure by exploiting the Ruppeiner geometry, where the thermodynamic curvature scalar is constructed via adiabatic compressibility. The nature of the curvature scalar along the coexistence line of small black hole (SBH) and large black hole (LBH) is investigated. In the microscopic interaction, we observe that the SBH phase behaves as an anyonic gas and the LBH phase is analogous to a boson gas. Further, we study the effect of graviton mass on the underlying microstructure of the black hole.