Role of Anisotropy and Higher-Order Curvature in the Stability of Sphere-like Charged Compact Structures

Source abstract

The dynamical stability of charged, anisotropic compact stellar objects is investigated under influence of tangential hyperbolic $f(R)$ gravity model, i.e., $f(R)=R-\varpi\Psi_{c}\tanh\left(\frac{R}{\Psi_{c}}\right)$, with anisotropic coupling. By employing a linear perturbation scheme, the modified field equations are decomposed into static and non-static sectors, leading to a collapse equation that connects energy density, anisotropic pressures, and the stiffness parameter $\Gamma$. Stability criteria are derived at both Newtonian and post-Newtonian regimes under suitable physical constraints. The analysis demonstrates that additional curvature terms and anisotropy significantly modify the instability ranges, while the adiabatic index $\Gamma$ determines the critical thresholds for collapse. The results are shown to be consistent with general relativity in the limiting case $\varpi \to 0$ and reduce to known results in the literature. This study provides further insights into the role of modified gravity corrections and anisotropic effects on the fate of charged compact stars.