Noncommutative inspired black holes in regularised 4D Einstein-Gauss-Bonnet theory

TL;DR

This paper constructs a noncommutative geometry inspired black hole solution within the regularized 4D Einstein-Gauss-Bonnet gravity, revealing modified thermodynamics, phase transitions, and a stable extremal black hole due to higher curvature corrections.

Contribution

It introduces a novel noncommutative inspired black hole solution in regularized 4D EGB gravity, analyzing its properties and thermodynamics, which has not been previously explored.

Findings

The black hole metric interpolates between a de Sitter core and EGB geometry.

Thermodynamic quantities are altered by noncommutativity and GB terms.

Phase transitions are characterized by a discontinuity in specific heat, leading to stable extremal black holes.

Abstract

Low energy limits of string theory indicated that the standard gravity action should be modified to include higher-order curvature terms, in the form of dimensionally continued Gauss-Bonnet densities. If one includes only quadratic curvature terms then the resulting theory is Einstein-Gauss-Bonnet (EGB) gravity valid only in $D>4$ dimensions. Recently there has been a surge of interest in regularizing, a $ D \to 4 $ limit, of EGB gravity, and the resulting regularized $4D$ EGB gravities have nontrivial gravitational dynamics. We obtain a static spherically symmetric noncommutative (NC) geometry inspired black hole solution with Gaussian mass distribution as a source in the regularized $4D$ EGB and also analyze their properties. The metric of the NC inspired $4D$ EGB black hole smoothly interpolates between a de Sitter core around the origin and $4D$ EGB metric as $r/\sqrt{\theta} \to \infty$. Owing to the NC and GB term corrected black hole, the thermodynamic quantities have also been altered. The phase transitions for the local thermodynamic stability, in the theory, is outlined by a discontinuity of specific heat $C_{+}$ at a critical radius $r_+=r_C$, and $C_{+}$ changes from infinitely negative to infinitely positive and then down to a finite positive for the smaller $r_+$. The thermal evaporation process leads to a thermodynamic stable extremal black hole with vanishing temperature.