Thermodynamic topology of topological charged dilatonic black holes

TL;DR

This paper investigates the thermodynamic topology of topological charged dilatonic black holes, analyzing how parameters like the topological constant influence their thermodynamic properties and comparing with charged black holes in General Relativity.

Contribution

It introduces a novel analysis of the thermodynamic topology of dilatonic black holes considering different ensembles and the impact of the topological constant, expanding understanding beyond standard charged black holes.

Findings

Thermodynamic topology depends on the topological constant and ensemble type.

Parameters of dilaton gravity significantly influence the black holes' thermodynamic structure.

Differences identified between dilatonic and standard charged black holes in topology.

Abstract

The aim of this paper is to explore the thermodynamic topology of topological charged dilatonic black holes. To achieve this, our study will begin by examining the characteristics of topological charged black holes in dilaton gravity. Specifically, we will concentrate on the impact of the topological constant on the event horizon of these black holes. Subsequently, we will analyze these black holes, considering their thermodynamic and conserved quantities, in order to assess the validity of the first law of thermodynamics. We explore the thermodynamic topology of these black holes by treating them as thermodynamic defects. For our study, we examine two types of thermodynamic ensembles: the fixed $q$ ensemble and the fixed $\phi$ ensemble. To study the impact of the topological constant ($% k$) on thermodynamic topology, we consider all possible types of curvature hypersurfaces that can form in these black holes. By calculating the topological charges at the defects within their thermodynamic spaces, we analyze both the local and global topology of these black holes. We also investigate how the parameters of dilaton gravity affect the thermodynamic topology of black holes and highlight the differences compared to charged black holes in the General Relativity.