Bardeen black hole thermodynamics from topological perspective

In this paper, we use the generalized off-shell Helmholtz free energy method to explore the thermodynamic properties of Bardeen black holes (BD BHs) from a topological perspective based on Duan’s topological current ϕ -mapping. We consider various structures of BD BHs, including regular BD-AdS BHs, BD-AdS BHs in Kiselev’s model of quintessence , BD BHs in massive gravity (MG), and BD BHs in 4D Einstein–Gauss–Bonnet (EGB) gravity. We demonstrate that these BHs have one topological classification (TC), i.e., TC is +1 for all BHs considered, and the addition of MG or GB terms, etc., does not change the topological numbers. • Studying the generalized off-shell Helmholtz free energy method for BD BHs • Studying the topological classification for Bardeen black holes • Various structures of BD BHs have one topological classification, i.e., TC is +1 • The addition of MG or GB terms, etc., does not change the topological numbers

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