Curvature-Regulated Gravitational Collapse: From Minimal Kinetic Theories to Covariant Dynamical Suppression

We investigate whether curvature growth in gravitational collapse can be dynamically regulated within a covariant effective field theory (EFT) without introducing additional propagating degrees of freedom. Building on previous work establishing the limitations of minimal quadratic kinetic theories, we introduce a curvature-dependent suppression mechanism that modifies the nonlinear structure of the stress-energy tensor in strong-field regimes.

We show that minimal P(X) theories admit finite-curvature attractors in homogeneous settings but fail to enforce curvature saturation in fully nonlinear inhomogeneous collapse. We then demonstrate that curvature-dependent kinetic suppression introduces a dynamical feedback mechanism that weakens gravitational focusing at high curvature.

Using double-null numerical evolution, we find that the regulator dynamically activates and replaces runaway amplification and mass inflation with bounded nonlinear evolution. At the analytical level, we formulate the system as a quasilinear hyperbolic partial differential equation (PDE), derive energy estimates, and obtain a curvature evolution inequality exhibiting a stable finite-curvature attractor.

These results identify curvature-dependent kinetic suppression as a minimal covariant mechanism required to control curvature growth once standard kinetic theories fail, providing a self-consistent pathway toward nonsingular gravitational dynamics within the regime of validity of effective field theory.