Novel topological subclasses of a magnetic black hole in causal nonlinear electrodynamics

By treating black-hole states as topological defects in thermodynamic parameter space, we investigate a static, asymptotically flat magnetic black holes in Einstein gravity coupled to causal nonlinear electrodynamics. Using the generalized off-shell free energy and Duan's $ϕ$-mapping topological current theory, we analyze the physical single-horizon sector in the canonical ensemble. We identify four representative defect-curve profiles, including realizations of the conjectured $W^{0+\leftrightarrow1-}$ class and $\overline{W}^{1-}$ subclass, as well as a new thermodynamic topological subclass, $\overline{W}^{0+\leftrightarrow1-}$. This new subclass features paired generation and annihilation points, with unstable innermost and outermost branches. As the auxiliary inverse temperature increases, the system evolves from two equilibrium states to three and then back to one, with an unstable small-black-hole defect entering through the physical lower boundary and changing the global topological number from $W=0$ to $W=-1$. This boundary-induced change signals a thermodynamic topological phase transition. These results show that the same inverse-temperature endpoint behavior and winding-number sequence from small to large black holes can accompany different defect evolution, highlighting the role of the physical horizon boundary in thermodynamic topological classification. More broadly, this causal nonlinear-electrodynamics black-hole family provides a setting for discovering further defect structures and thermodynamic topological phase transitions.