Stability and Topological Thermodynamics of Specific Black Holes

Abstract

In this thesis, we explore the charged higher-dimensional black holes by employing the Sharma-Mittal entropy which is widely used in black hole thermodynamics due to the non extensive nature of black holes. We compute different thermodynamic quantities like tem perature, heat capacity, and Gibbs free energy to study the stability of higher-dimensional black holes in Einstein-Gauss-Bonnet gravity. We explicitly analyze the behavior for differ ent horizon topologies (parameterized by k) in Einstein-Gauss-Bonnet gravity and observe that these black holes exhibit both local and global instabilities. Furthermore, to support our analysis, we chose thermodynamical topology methods (specifically the temperature and on-shell Gibbs free energy) to observe the stability of aforementioned black hole so lutions. It is found that the total topological charge obtained from the free energy method leads to +1for specific values of k which also gives the confirmation of the stability of these black hole solution in Einstein-Gauss-Bonnet gravity for specific choice of other constant parameters. Additionally, we study the sparsity of Hawking radiation, noting that the spar sity parameter tends to zero as the horizon radius increases. It is also observed that emission of energy radiates most rapidly for larger black holes which exhibits the consistency with physical observations.