Charged Cylindrical System and its Dynamical Instability under Expansion-free Condition in Rastall Theory

This study investigates the instability of a charged, cylindrically symmetric, expansion-free anisotropic fluid in the framework of Rastall gravity. A perturbation approach is used to obtain the dynamical equations of the system, allowing for a comprehensive stability analysis across the Newtonian, post-Newtonian, and post-post-Newtonian regimes. Our research shows that neither the Newtonian nor the post-Newtonian regimes’ instability requirements are affected by the adiabatic index, which is claimed to be a gauge of fluid stiffness. We deduce that a unique collection of parameters controls the instability, and their behavior closely matches with the well-established findings on gravitational collapse in different theoretical scenarios. The Darmois-Israel junction conditions are used which ensure a smooth matching between the interior and a suitable exterior geometry. We finally show that certain quantities such as the energy density, the three primary stresses, and an electric charge fundamentally determine the (in)stability requirements for the cylindrical system.