Non-extensive entropic corrected thermal stability and geometries of well-known black holes

In this study, we investigate the thermodynamic stability and geometries of well-known black holes such as the spherical static black hole, charged Einstein-Gauss-Bonnet black hole and R-N black hole of the dyadosphere in the presence of Barrow and Gauss-Bonnet entropy. We also investigate the stable/unstable region and phase transitions of these black holes using heat capacity. Furthermore, we investigate the thermodynamic geometries of the aforementioned black holes using different approaches, including Ruppeiner, Weinhold, Quevedo I, II, and HPEM. We observed that the divergence points of these approaches correspond to the phase transition points of heat capacity. Our investigation also concentrates on the influence of entropy parameters and the sparsity of Hawking radiation on the evaporation of black holes. It is observed that these black holes along with particular entropies give attractive/repulsive behavior. We also evaluate the physical consequences emerging by these black holes through the sparsity parameter.