Structure of $3D$ gravastars in the context of massive gravity

Abstract: In this paper, we investigate a new model of $(2+1)-$dimensional ($3D$) gravitational vacuum stars (gravastars) with an isotropic matter distribution anti-de Sitter (AdS) spacetime in the context of massive gravity. For this purpose, we explore free singularity models with a specific equation of state. Using Mazur-Mottola's approach, we predict $3D$ gravastars as alternatives to BTZ black holes in massive gravity. We find analytical solutions to the interior of gravastars free of singularities and event horizons. For a thin shell containing an ultra-relativistic stiff fluid, we discuss length, energy, and entropy. In conclusion, the parameter of massive gravity plays a significant role in predicting the proper length, energy contents and entropyand parameters of gravastars.