Role of Non-conserved Gravity Theory on Stability Analysis of Dark Energy Stars

This paper establishes two different dark energy stellar solutions which characterize spherical structures under the Rastall gravity. We construct the modified Einstein field equations by taking into account a static interior spacetime. By applying two particular equations of state linking dark energy components with the ordinary matter, we derive solutions of the field equations. We still find the system to be under-determined, so two different models, namely the Finch-Skea and Tolman IV ansatz are assumed to close the field equations, which lead us to two different solutions. In both scenarios, we use junction conditions to find the constants at the sphere’s boundary. We then enlist specific requirements that, when satisfied, result in compact models that are physically feasible. We also use the calculated data of two stars such as 4U 1538-52 and Her X-1 along with various Rastall parametric values to graphically asses our models. It is concluded that both stellar solutions satisfy the requirements needed for their physical existence under specific parametric choices.