Dynamics of collapsing charged compact fluid: A study in 𝒟-dimensional Einstein gravity

In this study, we investigate the dynamical behavior of charged sphere systems with anisotropic matter distribution. This systematic investigation is carried out under the influence of [Formula: see text]-dimensional Einstein gravity by using a perturbation scheme. We discuss the basic formalism of considered gravity with electromagnetic effects. Additionally, we develop matching criteria that guarantee the continuation of the first and second fundamental forms across the boundary [Formula: see text]. We compute the collapse equation by imposing certain conditions to establish the expression for the adiabatic index with the flat and curved background, which emphasizes the crucial role of the adiabatic index to discuss dynamical instability, as it characterizes the stiffness of the fluid and influences the ranges of instability. The analysis explores how factors such as anisotropic pressure, electric charge intensity, kinematic variables, mass function, parameters from [Formula: see text]-dimensional Einstein gravity, and the radial distribution of energy density affect the evolution and dynamics of considered spherical structures. The study includes visual representations to illustrate the influence of these properties on the spheres’ behavior over time. We investigate the existence of charge and how it may alter the stability zone of relativistic sphere-like formations with anisotropic matter distribution. We propose that a charged compact model may be more stable than an uncharged one, with a suitable choice of parametric values in [Formula: see text]-dimensional Einstein gravity.