Stable regions of anisotropic stellar structures via cracking and overturning

This study aims to elucidate the effects of density variations on the stability of spherically symmetric anisotropic stellar objects by examining the cracking phenomenon within the framework of Rastall gravity. The analysis focuses on anisotropic matter distributions described by the barotropic equation of state. Initially, the field equations and the Tolman–Oppenheimer–Volkoff (TOV) equation were formulated, and the Krori–Barua approach was employed. Subsequently, the equilibrium state of the stellar configuration was perturbed by introducing local density fluctuations. To validate the proposed methodology, the study analyzed various stars, including Cen X-3, Vela X-1, Her X-1, PSR J1614-2230, SAX J1808.4-3658, RXJ1856-37, and 4U 1820-30. The results demonstrate the presence of either the cracking or overturning phenomenon in all the analyzed stars. This investigation underscores the importance of incorporating the cracking method for a comprehensive stability analysis of stellar objects.