Linearized stability analysis of gravastars in noncommutative geometry

TL;DR

This paper constructs exact gravastar models within noncommutative geometry, analyzes their physical properties, and demonstrates their stability under radial perturbations, especially near the horizon formation region.

Contribution

It introduces new gravastar solutions in noncommutative geometry and investigates their stability, extending previous models by incorporating quantum geometric effects.

Findings

Stable gravastar configurations exist near the horizon.

Large stability regions are identified for certain parameter ranges.

Solutions are matched to Schwarzschild exterior spacetime.

Abstract

In this work, we find exact gravastar solutions in the context of noncommutative geometry, and explore their physical properties and characteristics. The energy density of these geometries is a smeared and particle-like gravitational source, where the mass is diffused throughout a region of linear dimension $\sqrt{(\alpha)}$ due to the intrinsic uncertainty encoded in the coordinate commutator. These solutions are then matched to an exterior Schwarzschild spacetime. We further explore the dynamical stability of the transition layer of these gravastars, for the specific case of $\beta=M^2/\alpha<1.9$, where M is the black hole mass, to linearized spherically symmetric radial perturbations about static equilibrium solutions. It is found that large stability regions exist and, in particular, located sufficiently close to where the event horizon is expected to form.