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.
Highlights
In the gravastar model, the interior consists of a segment of the de Sitter geometry, enclosed by a shell of Bose–Einstein condensate, all of which is surrounded by a Schwarzschild vacuum but without encountering a horizon
We explore the exact gravastar solutions in three-dimensional anti-de Sitter space given in the same geometry
The interior consists of a segment of the de Sitter geometry, enclosed by a shell of Bose–Einstein condensate, all of which is surrounded by a Schwarzschild vacuum but without encountering a horizon
Summary
The interior consists of a segment of the de Sitter geometry, enclosed by a shell of Bose–Einstein condensate, all of which is surrounded by a Schwarzschild vacuum but without encountering a horizon. It is interesting to reduce the number of spatial dimensions by 1 and to study general relativity in the simpler context of (2 + 1) dimensions in the hope that it has the potential to generate non-trivial and valuable insight into some of the conceptual issues that arise in the (3 + 1) dimensional case, especially in regard to the question of quantizing gravity. The usefulness of (2 + 1)dimensional gravity motivated us to show that neutral gravastars solutions do exist to avoid the event horizon formation, which may be considered as an alternative to BTZ in the context of noncommutative geometry.
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