Impact of Tolman-Kuchowicz metric potentials on cracking and overturning

Abstract

The purpose of this paper is to present the detailed analysis of the cracking/overturning technique to provide an extended perspective to comprehend how local density perturbations influence the stability of stellar structures exhibiting spherical symmetry within the Rastall gravity framework. For our current analysis, we analyze an anisotropic configuration governed by the barotropic equation of state and formulate the field equations. Following this, we incorporate the non-conservation of energy momentum tensor and derive the Tolman-Oppenheimer-Volkof equation. Further, we incorporate Tolman-Kuchowicz spacetime in our study and obtain the expression for radial forces to examine the occurrence of overturning and cracking by inducing disruptions to the configuration using local density perturbations. To verify the viability of this approach, we implement it to ten distinct stellar objects i.e., Her X-1, 4U 1538-52, SAX J1808.4-3658, PSR J1614-2230, SMC X-1, Cen X-3, Vela X-1, PSR J1903+0327, EXO 1785-248, and LMC X-4, revealing that each star undergoes overturning and cracking within the configuration. Conclusively, this work highlights the importance of utilizing the suggested cracking technique for stability analysis in compact objects.