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