Singularity-free dark energy star in Rastall gravity

Abstract

The notion of dark energy presents a potential avenue to avoid the gravitational collapse of compact objects, leading to singularities. The present article is devoted primarily to study a novel singularity-free relativistic solution of the Einstein field equations for dark energy stars in the framework of the Rastall theory of gravity. To analyse our model, we consider the Low-Mass X-ray Binary (LMXB) 4U 1608-52 having a mass of $1.74M_{\odot }$ and a radius of 9.3 km (Güver et al., 2010) as a possible dark energy star candidate. We begin with the dark energy equation of state, where the density of dark energy is proportional to the isotropic perfect fluid distribution through a coupling parameter $\alpha$. We compute the induced metric and extrinsic curvature tensors at the stellar hyper-surface to evaluate the necessary unknown constants appearing in the model. We conduct a thorough and comprehensive analysis to demonstrate the dependence of the physical behaviour of the model on the Rastall parameter $\left(\xi \right)$, and interestingly, we obtain a possible phase transition from the dark to baryonic profile, which is sensitive to both $\alpha$ and $\xi$. We also compute the percentage of dark energy present in the model by varying $\xi$. However, for a fixed value of $\xi$, the percentage variation of dark energy with the mass of a star shows that the percentage of dark energy depends on the mass and radius of a star. The causality and energy conditions are well met in the present model, which describes its physical acceptability. The stability of the stellar configuration is established through the study of stability analysis. The graphical nature of the physical parameters and the present theoretical study show that our proposed model is non-singular and a viable representation of a stable realistic stellar structure in the presence of dark and baryonic matter simultaneously.