Astrophysical signatures of exact anisotropic stellar solutions: Dynamics of two pulsars within the context of Rastall theory

Abstract

This study proposes a couple of analytical solutions that characterize the anisotropic dense celestial bodies within the Rastall theoretical framework. The analysis presumes a spherically symmetric matter arrangement under which the system of gravitational equations is derived. By utilizing well-established radial metric functions and merging them with the two principal pressures, we obtain differential equations related to $g_{tt}$ 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 LMC X-4 and 4U 1820-30. 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.