Role of Non-conserved Gravity Theory and Electric Charge in Constructing Complexity-free Stellar Models: A Novel Approach under Non-minimal Coupling

Abstract

This study explores the application of complexity factor within the context of Rastall gravity, exploring its implications on a static spacetime admitting spherical symmetry associated with anisotropic fluids under an electromagnetic field. The field equations are derived for a static charged sphere that provides a foundational framework for analyzing gravitational effects in this non-conserved theory. The mass function is formulated by incorporating both fluid and geometric parameters, offering insights into how mass distribution affects spacetime curvature. Through orthogonal decomposition of the Riemann tensor, a set of scalar quantities is obtained, referred to the structure scalars, which serve as indicators of celestial complexity. One specific scalar is then specified as the complexity factor, i.e., $\mathbb{Y}_{TF}$, facilitating further analysis on its role in characterizing complex systems. The presence of unknowns in gravitational equations necessitates the imposition of constraints to facilitate their solution. To address this, $\mathbb{Y}_{TF}=0$ alongside three distinct conditions are employed which yield diverse stellar models. A comprehensive graphical analysis is conducted using multiple values of the Rastall and charge parameters. Notably, the findings of this study align with those predicted by Einstein's theory. More appealingly, the Rastall theory demonstrates its superiority in the presence of charge under model 2 when it is compared with the general theory of relativity.