Non-commutative geometry and thermodynamics of the Schwarzschild-AdS black hole

TL;DR

This paper explores how noncommutative geometry influences the thermodynamics of Schwarzschild-AdS black holes, revealing phase transitions, van der Waals-like behavior, and the role of the noncommutativity parameter as a thermodynamic variable.

Contribution

It introduces the noncommutativity parameter {4d6} as a new thermodynamic variable and analyzes its effects on black hole thermodynamics and phase transitions.

Findings

Thermodynamic functions depend critically on the noncommutativity parameter.

Black hole undergoes a phase transition at a critical point.

Thermodynamic behavior resembles that of a van der Waals fluid.

Abstract

We investigate the thermodynamic properties of a Schwarzschild-AdS black hole within the framework of noncommutative geometry. We derive and analyze the black hole's thermodynamic functions, showing that they depend critically on the noncommutativity parameter denoted as {\Theta}, while still satisfying the first law of thermodynamics. Stability analysis reveals that the noncommutative Schwarzschild-AdS black hole undergoes a phase transition at a critical point. Moreover, the thermodynamic behavior closely resembles that of a van der Waals fluid, with the noncommutativity introducing a correction term to the black hole's surface temperature. Our results indicate that the noncommutativity parameter {\Theta} is of the order of the Planck scale and functions as a novel thermodynamic variable within the system.