Stability analysis of Lower Dimensional Gravastars in noncommutative geometry

TL;DR

This paper constructs and analyzes the stability of lower-dimensional gravastar solutions within noncommutative geometry, extending BTZ black hole models to include smeared matter distributions and examining their stability under radial perturbations.

Contribution

It presents exact gravastar solutions in 3D anti-de Sitter space with noncommutative geometry, including stability analysis under radial perturbations, which is a novel extension of BTZ black hole models.

Findings

Stable gravastar configurations identified for certain parameter ranges.

Smeared matter distributions modeled with Gaussian functions.

Stability depends on the parameter , with specific bounds for stability.

Abstract

The Ba\~{n}ados, Teitelboim and Zanelli \cite{BTZ1992}, black hole solution is revamped from the Einstein field equations in (2 + 1)-dimensional anti-de Sitter spacetime, in a context of noncommutative geometry \cite{Rahaman(2013)}. In this article, we explore the exact gravastar solutions in three-dimension anti-de Sitter space given in the same geometry. As a first step we derive BTZ solution assuming the source of energy density as point-like structures in favor of smeared objects, where the particle mass M, is diffused throughout a region of linear size $\sqrt{\alpha}$ and is described by a Gaussian function of finite width rather than a Dirac delta function. We matched our interior solution to an exterior BTZ spacetime at a junction interface situated outside the event horizon. Furthermore, stability analysis is carried out for the dynamic case for the specific case when $\chi < 0. 214$ under radial perturbations about static equilibrium solutions. To give theoretical support we also trying to explore their physical properties and characteristics.