On Thermodynamics of Charged Black Holes via Extended Space-time Derivatives

TL;DR

This paper explores the thermodynamics of charged black holes influenced by extended derivatives inspired by string theory, revealing Van der Waals-like phase transitions and parameter constraints through numerical analysis.

Contribution

It introduces extended derivatives in black hole physics based on non-commutative geometry, deriving new solutions and analyzing their thermodynamic phase behavior.

Findings

Black hole solutions exhibit Van der Waals phase transitions.

Parameter constraints identified for B and Q for Van der Waals behavior.

Numerical methods confirm stability and criticality regions.

Abstract

Inspired by non-commutative geometry in string theory, we propose extended derivatives in black hole physics by incorporating a real antisymmetric tensor of rank 2 carrying similarities of certain stringy fields. Using gauge theory formulation of gravity via de Sitter group theory, we first find the associated black hole solutions by solving the Einstein field equations. Then, we study the thermodynamic properties by approaching the stability analysis, the criticality, and the phase transitions. Concretely, we investigate the P-V criticality behavior of the obtained solution. We compute and examine the Gibbs free energy revealing comparable attitudes with the Van der Waals phase transitions. Combining such results, we provide constraints on the deformed parameter B and the charge Q with the help of CUDA numerical methods exploited in machine learning computations. Precisely, we show that there are suitable ranges for such parameters where the obtained black holes behave like the Van der Waals fluid systems.