Novel topological subclass in Ho\u{r}ava-Lifshitz black holes

This work explores the universal classification of thermodynamic topology for charged static black holes within the $z=3$ Ho\u{r}ava-Lifshitz gravity theory, considering both canonical and grand canonical ensembles. We introduce a new topological subclass, denoted as $\ddot{W}^{1-}$. This finding expands the existing topological classification, going beyond the five previously defined classes and their respective subclasses. The $\ddot{W}^{1-}$ subclass presents a distinct and previously unobserved stability profile: In the low-temperature regime, an unstable small black hole appears in the phase space, whereas, while in the high temperature regime, two unstable small black holes exist together with a stable large black hole. Our study underscores the dependence of charged black hole stability on the selection of the ensemble. These results contribute to refining and expanding the topological framework in black hole thermodynamics, providing key perspectives on the underlying nature of black holes and gravity.