Thermodynamic geometry and Joule-Thomson expansion of black holes in modified theories of gravity

The implication of Ruppeiner thermodynamic geometry theory to spherically symmetric black holes in anti-de Sitter (AdS) spacetime produces an unavoidable singularity in the line element of thermodynamic geometry. The singularity occurs due to the nonindependence of volume and entropy of black holes (BH) in AdS spacetime. In this work, we present an efficient and easy approach to deal the thermodynamic geometry of AdS BH in Einstein-Maxwell-scalars theory. We show that enthalpy instead of internal energy is central thermodynamic quantity. We develop the particular forms of the line element of thermodynamic geometry in different phase spaces. We find out that the curvatures in different phase spaces are identical and positive which leads to the repulsive interaction information between black hole molecules. We also analyze the thermal stability of AdS BH in Einstein-Maxwell-scalars theory and regularized Lovelock theory in the presence of thermal fluctuations. We observed that momentum relaxation parameter and coupling constants of Lovelock theory increase the thermal stability of the BHs. Finally, we also study the Joule-Thomson expansion for black hole in regularized Lovelock theory.