Entropy and Irreversibility in Bounded-Curvature Spacetime

As Classical General Relativity (GR) is time-reversal symmetric, yet gravitational collapse and compact-object mergers exhibit pronounced irreversibility. In standard treatments, this behaviour is attributed to singularities, coarse-graining, or special initial conditions. In bounded-curvature spacetime, where curvature invariants possess a universal upper bound and geometric response is progressively suppressed near that bound, the origin of irreversibility must be reconsidered. This work argues that an effective arrow of time emerges as a direct geometric consequence of bounded curvature. saturation is approached, spacetime evolution ceases to be invertible: saturated states defined as configurations in which curvature invariants reach the saturation bound introduced in Ref. [1]-lie on the boundary of admissible geometric phase space and do not admit valid inverse nverse trajectories. Dissipation remains permitted because it operates entirely in sub-saturated, geometrically responsive regions and removes the external forcing that maintains saturated domains, without reversing saturated geometry itself. Irreversibility is therefore structural rather than statistical, and arises without invoking information destruction or microscopic time asymmetry.