Compact Objects and Curvature Saturation

Compact Objects and Curvature Saturation Neutron Stars as Probes of Saturation Onset If spacetime admits a universal bound on curvature, then the approach to that bound must modify gravitational response before singular behaviour occurs. While full curvature saturation is expected only deep inside black hole interiors, the onset of saturation effects may occur at lower curvature and could influence the structure and stability of compact, horizonless objects. In this work we examine neutron stars as natural probes of the onset regime of curvature saturation. Without assuming a specific equation of state, rotation profile, or microphysical model, we analyze how a gradual suppression of geometric responsiveness near the saturation scale modifies classical collapse thresholds. We show that neutron stars primarily constrain the shape and accessibility of the saturation onset rather than the existence of saturation itself. Possible outcomes include unchanged GR-like behaviour, modest shifts in the maximum stable mass, delayed collapse, or—under restricted conditions—the existence of near-saturated equilibrium cores. These results establish compact objects as a consistency test of bounded-curvature spacetime and motivate dynamical studies of mergers as the next critical regime.