Thermodynamic topological classification of magnetically charged slowly rotating Kerr black holes in nonlinear electrodynamics with a cosmological constant

Abstract

In this work, we investigate the thermodynamic topological classification of slowly rotating Kerr black holes with magnetic charge in nonlinear electrodynamics (NLED) using a reduced grand-canonical off-shell prescription. By constructing the generalized off-shell free energy and the associated topological vector field, we determine the local winding numbers and the global topological charge of the NLED-Kerr black hole in both de Sitter (dS) and anti-de Sitter (AdS) spacetimes. The inverse-temperature curve starts from a finite nonzero value at the lower radial endpoint and diverges at large horizon radius. Together with the single zero of winding number $w=-1$, this behavior identifies the black hole as a realization of the predicted \(\overline{W}^{1-}\) subclass, with global topological number $W=-1$ and a single unstable branch. The classification remains unchanged over the sampled rotation, NLED, and magnetic-charge parameters. Within the same prescription, comparison with the two-branch $W^{0-}$ Kerr-AdS result associates the NLED effective mass function with the changed endpoint behavior and the absence of a stable large-black-hole branch. Thus, the physical novelty is an explicit rotating NLED realization of the predicted \(\overline{W}^{1-}\) subclass for both signs of the cosmological constant.