Dynamical Analysis of a Charged Spherical Star in \(\boldsymbol{R-}\boldsymbol{\beta}\boldsymbol{R}_{\boldsymbol{c}}\mathbf{tanh}\boldsymbol{(R/R_{c})+}\boldsymbol{\xi}\boldsymbol{RT}\) Gravity

We illustrate the dynamical instability of charged spherical fluid configuration with anisotropic conditions in nonminimally coupled \(f(R,T)\) theory of gravitation, where \(R\) is the Ricci scalar and \(T\) is the trace of the energy momentum-tensor. We investigate both modified field equations and continuity equations to provide some extra degrees of freedom under the constraints of a specific considered form of \(f(R,T)\) gravity. We examine how small changes in geometric and material profiles affect the fluid’s collapsing structure via a perturbation scheme. We study the unstable eras using Newtonian (\(\mathbb{N}\)) and post-Newtonian (pN) approximations by applying some significant constraints on the collapse equation. Our findings demonstrate that the stiffness parameter \(\Gamma\) has a substantial influence on the identification of unstable phases for our charged stellar geometry. We conclude that some correction terms that are dark source terms, which appear due to \(f(R,T)\) gravity, lead to an unstable structure/phase throughout the evolutionary process.