GR--CS III: Finite Curvature and the Stopped--Clock Horizon

This paper extends the General Relativity–Clock Shift (GR-CS) framework to the domain of gravitational collapse and black-hole interiors. It introduces the concept of a finite-curvature “stopped-clock horizon,” where the scalar time field N(x) asymptotically approaches zero, halting local time progression without producing infinite curvature. In this formulation, gravitational collapse is governed by temporal compression rather than geometric singularity, preserving full consistency with Einstein’s field equations while eliminating divergence at the core. The horizon represents a limit surface of finite energy density and vanishing clock rate, yielding the same external observables as classical general relativity. This conceptual development marks the third stage of the GR-CS series, following Clock Differential Formulation of GR-CS and Clock Gradient Gravitational. It emphasizes the physical interpretation of gravity as modulation of time flow, offering a pathway to bridge classical GR with quantum information and thermodynamic boundary models.