Probing topological thermodynamics of specific black holes inspired by corrected entropy

Thermodynamics stability of various higher (five) dimensional black holes such as Euler-Heisenberg, non-linear electrodynamic, and Yang-Mills massive gravity is being investigated. Thermodynamic topology along with stability within their respective parameter spaces will also be addressed by employing exponential corrected entropy (non-extensive entropy). We manifest first-order phase transitions by finding critical points and topological charges through the ϕ -mapping method. Our comprehensive thermodynamic analysis incorporates key variables such as pressure, temperature volume and free energy. We observe notable result is the critical role played by the QED parameter ( a ) in Euler-Heisenberg black holes, which determines the existence of two distinct topological classes. It is also noted that non-linear electrodynamic fields inspired black holes parameters does not impact on the number of critical points or topological classes. For Yang-Mills black hole in massive gravity, it is found that there exists a unique topological structure with one critical point that depends on corresponding black hole parameter.

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