Isotropic compact stellar model in Rastall's gravitational theory

Abstract

Is Rastall's theory of gravity equivalent to Einstein's general relativity theory? This question has sparked a significant debate, prompting researchers to delve into the topic. To investigate further, we apply Rastall's theory's field equation to a spacetime characterized by spherical symmetry. This leads us to encounter a system of non-linear differential equations that is overdetermined. To address this, we make assumptions about the specific form of the metric potential's temporal component, denoted as gtt. Additionally, we impose constraints to eliminate the anisotropic condition, resulting in a vanishing effect. These steps allow us to determine the form of grr and ultimately achieve an isotropic spacetime. Furthermore, our investigation focuses on the potential of obtaining a set of parameters that align with the observed behavior of pulsars. To achieve this, we employ junction conditions to match the interior spacetime with the exterior Schwarzschild configuration, thereby constraining the model's relevant constants. Subsequently, we employ the pulsar SAXJ1748.9−2021, characterized by a measured mass of M=1.81±0.31,M⊙ and a radius of R=11.7±1.7 km, to numerically explore the physical properties of the model. Stability is assessed using the Tolman-Oppenheimer-Volkoff equation and the adiabatic index. Our findings suggest that Rastall's parameter, a key distinction of Rastall's theory from Einstein's general relativity, can play a crucial role in forming a realistic, compact object consistent with observational data. Furthermore, we verify the model's validity by comparing it with various observed masses and radii of different pulsars, ensuring a satisfactory fit between the model proposed in this study and the observed data.