Thermodynamics of a class of non-asymptotically flat black holes in Einstein-Maxwell-Dilaton theory

TL;DR

This paper investigates the thermodynamics of a specific class of non-asymptotically flat black holes in Einstein-Maxwell-Dilaton theory, revealing insights into their stability, geometric properties, and thermodynamic interactions.

Contribution

It provides the first detailed thermodynamic analysis of these black holes using multiple geometric methods and explores their stability characteristics.

Findings

Geometric methods show zero curvature scalar, conflicting with non-zero specific heat results.

The system is thermodynamically interacting without phase transitions or extremal states.

Stability depends on the parameter gamma, with a critical value at gamma=0 separating stable and unstable regimes.

Abstract

We analyse in detail the thermodynamics in the canonical and grand canonical ensembles of a class of non-asymptotically flat black holes of the Einstein-(anti) Maxwell-(anti) Dilaton theory in 4D with spherical symmetry. We present the first law of thermodynamics, the thermodynamic analysis of the system through the geometrothermodynamics methods, Weinhold, Ruppeiner, Liu-Lu-Luo-Shao and the most common, that made by the specific heat. The geometric methods show a curvature scalar identically zero, which is incompatible with the results of the analysis made by the non null specific heat, which shows that the system is thermodynamically interacting, does not possess extreme case nor phase transition. We also analyse the local and global stability of the thermodynamic system, and obtain a local and global stability for the normal case for 0<\gamma<1 and for other values of \gamma, an unstable system. The solution where \gamma=0 separates the class of locally and globally stable solutions from the unstable ones.