Geometry and topology of two kinds of extreme Reissner-Nordstr$\ddot{o}$m-anti-de Sitter black holes

TL;DR

This paper explores the geometric and topological features of two types of extreme Reissner-Nordström-anti-de Sitter black holes and clarifies their connection to thermodynamic properties.

Contribution

It provides a detailed analysis of the geometrical and topological differences and their relation to thermodynamics in these specific black hole solutions.

Findings

Distinct geometrical properties identified for the two black hole types

Explicit relationship established between geometry and thermodynamics

Topological differences characterized and analyzed

Abstract

Different geometrical and topological properties have been shown for two kinds of extreme Reissner-Nordstr$\ddot{o}$m-anti-de Sitter black holes. The relationship between the geometrical properties and the intrinsic thermodynamical properties has been made explicit.