Phase transition grade and microstructure of AdS black holes in massive gravity

Considering that under the framework of massive gravity theory, interaction between mass gravitons and Schwarzschild black hole (BH) could make it carry a scalar charge, phase transition process caused by this charge is investigated in analysis. The grade microstructure those BHs are from both macroscopic microscopic points view. From point view, found Ehrenfest equations satisfied at critical point, which implies second-order. Based on BH molecules model Landau continuous microcosmic view analyzed. exponents obtained two perspectives consistent. By investigating Ruppeiner geometry, feature revealed. These results suggest standard second-order details different RN-AdS Einstein gravity.