Anisotropic Spherical Solutions in Rastall Gravity by Gravitational Decoupling

TL;DR

This paper develops new anisotropic spherical solutions in Rastall gravity using gravitational decoupling, analyzing their physical viability, stability, and matching conditions with Schwarzschild exterior.

Contribution

It introduces a novel application of gravitational decoupling to generate anisotropic solutions in Rastall gravity, extending the Finch-Skea ansatz.

Findings

Solutions are physically viable under certain Rastall parameters.

Only pressure-like solutions are stable according to Herrera cracking.

The solutions satisfy energy conditions and exhibit realistic redshift and compactness.

Abstract

In this paper, we extend the Finch-Skea isotropic ansatz representing a self-gravitating interior to two anisotropic spherical solutions within the context of Rastall gravity. For this purpose, we use a newly developed technique, named as gravitational decoupling approach through the minimal geometric deformation. The junction conditions that provide the governing rules for the smooth matching of the interior and exterior geometries at the hypersurface are formulated with the outer geometry depicted by the Schwarzschild spacetime. We check the physical viability of both solutions through energy conditions for two fixed values of the Rastall parameter. The behavior of the equation of state parameters, surface redshift and compactness function are also investigated. Finally, we study the stability of the resulting solutions through Herrera cracking approach and the causality condition. It is concluded that the chosen parametric values provide stable structure only for the solution corresponding to the pressure-like constraint.