We study relativistic solutions of anisotropic compact stars with Finch-Skea (FS) metric in f (T) gravity framework. The modified FS geometry is considered to obtain the equation of state (EoS) for different known stellar objects with given mass and radius. The modified Chaplygin gas (MCG) EoS is also considered to obtain stellar objects as the EoS inside the star is not yet known. The results obtained here is important in the two cases to understand properties of known stars, which are however not known observationally. The physical features of known stars are analyzed here and found that compact star formation may be possible with repulsive core. In the case of MCG in f (T) gravity compact stars may be obtained with anisotropic fluid (p t > p r), with maximum anisotropy at the center of the star, which however is not found when MCG is absent.

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 [1,2] 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 [3,4]. 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.

We obtain relativistic solutions of anisotropic charged compact objects in hydrodynamical equilibrium with Finch–Skea geometry in the usual four and in higher dimensions. The relativistic solutions are employed to construct physically viable stellar models. The radial variations of density, pressure and other different physical features inside the stars are studied in the relativistic stellar models. It is noted that a compact star in four-dimensional Finch–Skea geometry describes an isotropic uncharged star always which however predicts existence of an anisotropic star in higher dimensional spacetime. The plausibility of such stars are studied here for a given mass and radius. Considering known compact objects we construct stellar models satisfying all the criteria of a physically realistic star. The results obtained here may be important to understand some of the physical properties of known stars including predictions of equations of states at extreme conditions.

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