Study of Gravastars in Rastall Gravity

Gravastars have been considered as a feasible alternative to black holes in the past couple of decades. Stable models of gravastar have been studied in many of the alternative gravity theories besides standard General Relativity (GR). The Rastall theory of gravity is a popular alternative to GR, specially in the cosmological and astrophysical context. Here, we propose a stellar model under the Rastall gravity following Mazur-Mottola's \cite{Mazur2001,Mazur2004} conjecture. The gravastar consists of three regions, viz., ($I$) Interior region, ($II$) Intermediate shell region, and ($III$) Exterior region. The pressure within the interior core region is assumed with a constant negative matter-energy density which provides a repulsive force over the entire thin shell region. The shell is assumed to be made up of fluid of ultrarelativistic plasma which follows the Zel'dovich's conjecture of stiff fluid \cite{Zeldo1962,Zel'dovich1972}. It is also assumed that the pressure is proportional to the matter-energy density according to Zel'dovich's conjecture, which cancel the repulsive force exerted by the interior region. The exterior region is completely vacuum which is described by the Schwarzschild-de Sitter solution. Under all these specifications we obtain a set of exact and singularity-free solutions of the gravastar model presenting several physically valid features within the framework of Rastall gravity. The physical properties of the shell region namely, the energy density, proper length, total energy and entropy are explored. The stability of the gravastar model is investigated using the surface redshift against the shell thickness and maximizing the entropy of the shell within the framework of Rastall gravity.