Joule Thomson expansion, Maxwell equal area law and topological interpretation of Phantom RN AdS black holes

This paper is devoted to study the thermodynamic topological defects, Joule–Thomson ($J-T$) and Maxwell’s equal area law of Phantom RN AdS black holes (BHs). The inversion temperatures and inversion curves are obtained and by using the isenthalpic curves in the temperature–pressure ($T-P$) plane to locate the cooling and heating regions. Using Maxwell’s equal-area law, we select different independent conjugate variables to study the phase transitions of Phantom RN AdS BHs. We find that phase transition rely on the electric potential and horizon radius of the BH when its charge is constant. Phase transition of Phantom RN AdS BH are proportional to the ratio of event horizon to its cosmological constant, where the latter is assumed to be constant. Moreover, we consider the Phantom RN AdS BH as defects with a topological nature within thermodynamic domain and examine the local and global topology by computing the winding numbers at the defects, which concludes that the overall topological charge is either equal to 0 or 1.