Thermal geometries and the Joule–Thomson expansion of modified charged and slowly rotating black holes

Thermodynamics of charged and slowly rotating black holes in 4D Gauss–Bonnet gravity has attracted a great deal of attention due to its intrinsic complications and rich phase structures. In this paper, we revisit the thermodynamics of charged and slowly rotating black holes and provide the correct thermodynamic volume and entropy. Thermodynamic geometries are a powerful tool to study the microstructure of black holes. Based on the Hessian matrix of the black hole mass, we introduce thermodynamic geometric methods and give its scalar curvature (Ruppeiner and Weinhold). Furthermore, we investigate the Joule–Thomson expansion of slowly rotating black hole in 4D Gauss–Bonnet gravity in this research study. Interestingly, we explicitly state that the expression of the Joule–Thomson coefficient is obtained from the basic formulas of enthalpy and temperature. Then, we obtain the isenthalpic curve in the T − P graph and demonstrate the cooling–heating region by the inversion curve. The inversion temperature and inversion curves are obtained, and we investigate the similarities and differences between van der Waals fluids and charged fluids.