Effective Perturbation Dynamics Near Curvature Saturation

Effective Perturbation Dynamics Near Curvature Saturation This work develops a minimal effective framework to describe the evolution of perturbations as spacetime approaches and exits a regime of curvature saturation. Introducing a geometric response function that smoothly interpolates between General Relativity and a stiff, non-responsive limit, we construct toy evolution equations that capture the essential dynamical consequences of bounded curvature. Asymptotic freeze-out of perturbations near saturation emerges as a structural feature independent of detailed microphysics, leading to generic suppression of pre-saturation structure. The framework applies to both black hole interiors and early-universe cosmology, providing mathematical guard rails for future, model-dependent investigations.