Existence and stability of (3+1)-dimensional gravastar model in de Rham–Gabadadze–Tolley like massive gravity

The physical properties of a (3+1)-D gravastar in the context of massive gravity are discussed in this work. In present investigation, the field equations have been solved for a static, uncharged sphere in order to achieve the gravastar model as proposed by Mazur and Mottola [Mazur and Mottola in Report No. LA-UR-01-5067, (2001); Mazur and Mottola, Proc. Natl. Acad. Sci. USA 101 (2004) 9545]. We address length of thin shell, energy, and entropy for the thin shell containing an ultra-relativistic stiff fluid. Israel matching criteria are used to ensure that the inner and outside geometries join smoothly. The present study within dRGT gravity differs markedly and fundamentally from true gravastars described in [arXiv:2302.09690; Mazur and Mottola, Class. Quant. Grav. 32 (2015) 215024], which requires the phase transition occured at $R=2M$. It turns out that the existence of the graviton mass entirely alters the behavior of the gravastar. Particularly, when $m\to 0$, our findings precisely matched the outcomes of general relativity.