Dynamics of Compact Stellar Solutions Admitting Anisotropic Fluid: A Comparative Analysis of GR and Non-Conserved Rastall Gravity

This study proposes a couple of analytical solutions that characterize the anisotropic dense celestial bodies within the Rastall-Rainbow theoretical framework. The analysis assumes a static spherically symmetric matter distribution and derives the corresponding modified field equations. By utilizing well-established radial metric functions and merging them with the two principal pressures, we obtain differential equations related to the time component. Subsequently, we perform the integration of these equations to determine the remaining geometric quantity that encompasses various integration constants. The proposed interior solutions are then matched with the Schwarzschild exterior metric at the boundary of the compact object, facilitating the determination of the constants. Additionally, the incorporation of the non-minimal coupling parameter into these constants is accomplished by enforcing the null radial pressure at the boundary. Afterwards, we rigorously examine the physical characteristics and critical stability conditions of the formulated models under observational data from two pulsars, say 4U 1820-30 and LMC X-4. It is concluded that our models are well-aligned with essential criteria required to ensure the physical viability of stellar structures, subject to specific parametric values.