Curvature-Regulated Matter Sourcing and Asymptotic Gravitational Collapse in General Relativity

We present a minimal classical deformation of general relativity in which the Einstein–Hilbert gravitational sector remains unchanged, while the matter sector acquires a curvature-dependent regulator characterized by a single curvature scale R*. The modification alters effective stress–energy sourcing only at high curvature and reduces exactly to general relativity in all weak-field regimes. The field equations remain second-order, introduce no additional propagating degrees of freedom, and preserve covariant conservation. For homogeneous collapse, curvature dynamically saturates at a finite scale without invoking higher-derivative corrections. The construction provides a controlled classical extension of matter sourcing within general relativity.