Advanced Analysis of Hawking Temperature Calculation for Novel Topological Black Holes using Laurent Series and the RVB Method

This paper employs Laurent series expansions and the Robson--Villari--Biancalana (RVB) method to provide a refined derivation of the Hawking temperature for two newly introduced topological black hole solutions. Previous calculations have demonstrated inconsistencies when applying traditional methods to such exotic horizons, prompting the need for a more thorough mathematical analysis. By systematically incorporating higher-order terms in the Laurent expansions of the metric functions near the horizon and leveraging the topological features characterized by the Euler characteristic, we reveal additional corrections to the Hawking temperature beyond standard approaches. These findings underscore the subtle interplay between local geometry, spacetime topology, and quantum effects. The results clarify discrepancies found in earlier works, present a more accurate representation of thermodynamic properties for the black holes in question, and suggest broader implications for topological structures in advanced gravitational theories.