Implications of Rastall Theory on Stellar Solutions admitting Vanishing Complexity: A New Perspective

TL;DR

This paper explores how Rastall gravity affects stellar models with zero complexity, deriving new solutions and comparing their physical viability to general relativity, highlighting Rastall theory's advantages.

Contribution

It extends the concept of complexity factor to Rastall gravity, introduces constraints for stellar solutions, and demonstrates Rastall theory's potential superiority over Einstein's gravity.

Findings

Rastall theory yields physically consistent stellar models.

Model 2 shows more suitable results in Rastall gravity.

Results align with general relativity, with Rastall offering improvements.

Abstract

In this paper, the notion of complexity factor and its implication is extended to the framework of non-conserved Rastall theory of gravity. First of all, the field equations governing a static spherical geometry associated with the anisotropic fluid are formulated. The mass function corresponding to the considered geometry is defined in terms of both matter and geometric quantities. The orthogonal decomposition of the Riemann tensor is then performed through which a family of scalar quantities, known as structure scalars, is obtained. Using the Herrera's recent definition, one of the scalars among them is claimed as the complexity factor, \emph{i.e.}, $\mathcal{Y}_{TF}$. Since there are extra degrees of freedom in the gravitational equations, some constraints are needed to make their solution possible to obtain. In this regard, a well-known vanishing complexity condition is introduced along with three different constraints which ultimately lead to distinct stellar models. In order to check their physical feasibility, a detailed graphical interpretation is provided using multiple values of the Rastall parameter. It is concluded that the obtained results in all three cases are consistent with those of general relativity. Further, the Rastall theory provides more suitable results in the case of model 2, indicating its superiority over Einstein's gravity theory.