A comprehensive discussion for the identification of cracking points in f(R) theories of gravity

This paper investigates the concept of cracking and overturning to analyze the impact of local density perturbations on the stability of self-gravitating compact objects in the framework of f(R, ϕ, X) theory of gravity, where R, ϕ, and X denote the Ricci scalar, scalar potential, and kinetic term, respectively. In this context, we developed the hydrostatic equilibrium equation for spherically symmetric spacetime with anisotropic matter configuration and subsequently employed the Krori Barua technique. We then perturb the hydrostatic equilibrium state of the configuration by employing the local density perturbation technique, while taking into account the barotropic equation of state. To validate this technique, we employed it on different compact stars namely, Her X-1, SAX J1808.4-3658, 4U 1820-30, PSR J1614-2230, Vela X-1, and Cen X-3, and found that all stars exhibit cracking or overturning for a specific range of model parameters. Conclusively, this study emphasizes that the proposed cracking technique provides significant insights into the stability analysis of self-gravitating compact objects.