Dynamically Charged Spheres and their Stability in Einstein-Gauss-Bonnet Gravity

Electrically charged anisotropic fluid spheres with vanishing expansion scalar condition under the influence of a newly established gravitational scheme are investigated in this study, i.e., $4D$ Einstein-Gauss-Bonnet (EGB) gravity. Glavan and Lin introduced this framework, in which they rescaled the coupling factor $\alpha$ using $\frac{\alpha }{D-4}$ and derived the gravitational field equations. The work of Herrera et al. is extended to explore the dynamical instability of charged spherically symmetric matter distribution in the context of $4D$ EGB gravity. In this respect, dynamical equations, conservation equations, and junction conditions for charged sphere are computed. To study the evolution of considered system in the Newtonian and post-Newtonian regimes against an expansion-free background, several substantial restrictions are imposed employing a perturbation approach. This study showed that the adiabatic index ($\Gamma$) has no effect on the instability ranges in the aforementioned approximations. It is analyzed that the determination of these ranges solely attributed to the anisotropy of fluid surface pressures, radial profile, $4D$ EGB factors, and charged intensity parameters along with the radial distribution of energy density.