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 the adiabatic compressibility. The nature of the curvature scalar along the coexistence line of small (SBH) and large (LBH) black holes 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.