Abstract
In the context of minimally matter-geometry coupled gravity, the dynamical stability of axially symmetric, self-gravitating compact objects is investigated in this paper. We look into the nature of anisotropic star structures using a formalism of Hu-Sawicki inspired f(R,T) gravity and develop the related field and non-conservation equations. The perturbation approach is applied to these equations to construct the collapse equation governing the evolution of the compact system. The stability conditions are then established through the adiabatic index Γ in both N and pN eras, highlighting the consequence of matter geometry coupling on the equilibrium and collapse of compact configurations. The analysis exhibits that the inclusion of Hu-Sawicki corrections significantly modifies the classical instability limits, allowing a broader range of stable configurations for certain choices of model parameters. These outcomes offer more understanding on how modified gravity directs the gravitational collapse of anisotropic compact objects and explains cosmic evolutionary events that go beyond the boundaries of general relativity.