Novel thermodynamic topological subclass from inverse-temperature asymptotics

Abstract

We investigate the thermodynamic topology of the charged McGuigan--Nappi--Yost black hole in the canonical ensemble at fixed electric charge, identifying equilibrium black hole solutions as zeros of the thermodynamic vector field constructed from the generalized off-shell free energy. The inverse Hawking temperature diverges as the extremal limit is approached and approaches a finite positive value in the large-horizon limit. The zero points of the thermodynamic vector field reveal a thermodynamic phase structure consisting solely of a locally stable branch with positive winding number ($w=+1$). The innermost small black hole state is locally stable in the low-temperature limit. As the temperature increases, the stable branch extends toward the outermost large black hole regime, while no black hole states exist in the high-temperature regime beyond the finite upper Hawking temperature. This distinct asymptotic behavior of the inverse temperature places the thermodynamic defect structure outside the established topological (sub)classes, although its topological number agrees with that of the standard $W^{1+}$ class. We therefore identify this defect structure as a new thermodynamic topological subclass, $\breve W^{1+}$. This finding extends the existing classification to include a finite, nonzero large-horizon limit of the inverse Hawking temperature and suggests that distinct asymptotic behaviors in other black hole families may reveal further topological (sub)classes and thermodynamic phase structures.