Effects of minimally coupled modified gravity on the gravitational collapse of compact matter structures

Our analysis is particularly motivated by its relevance to understanding compact object instabilities, gravitational collapse thresholds, and the formation of dense structures under the influence of modified gravity theories. The interplay of anisotropic pressures, perturbative dynamics, and modified gravity contributions offers insight into both the stable configuration of dense fluids and the mechanisms leading to dynamical instability, whereas such considerations directly contribute to the aims of high energy density profiles, particularly in modeling physical systems where extreme pressure, curvature, and matter interactions co-exist. We consider an axially symmetric dense structure with anisotropic matter content and employ a peculiar equation of state to examine the interplay between static and dynamic quantities via the adiabatic index. To address the complex dynamics of the collapse process, a perturbative scheme is utilized under Newtonian and post-Newtonian approximations, enabling a detailed examination of the stability and structural evolution of the system under the influence of considered minimally coupled gravity. Our results demonstrate that hydrostatic equilibrium is maintained when effective pressure, gravitational, and anti-gravitational forces are balanced, while deviations from this balance initiate dynamical instability. Graphical representations of stable and unstable regimes are presented, revealing how the choice of gravity functions significantly affects the outcome. This work provides insight into the behavior of dense, self-gravitating configurations under modified gravity, offering broader implications for the modeling of compact astrophysical objects and contributing to the understanding of gravitational collapse in energy density regimes.