On the Semiclassical Stability of Cauchy Horizons: Renormalized Stress-Energy Tensor Bounds via Geodesic Mass Cutoffs

In this paper, we investigate the semiclassical stability of Cauchy horizons in spacetimes admitting Closed Timelike Curves (CTCs). We challenge the universality of Hawking's Chronology Protection Conjecture by introducing an invariant geodesic mass cutoff derived from the Generalized Uncertainty Principle (GUP). We demonstrate that the presence of a macroscopic mass traversing the horizon imposes a minimum proper time interval (\Delta\tau_{\text{min}}), which effectively regularizes the vacuum polarization divergences of the renormalized stress-energy tensor. Furthermore, by integrating Seth Lloyd’s post-selected CTC (P-CTC) framework, we show that the macroscopic mass acts as an environment, inducing rapid decoherence that preserves causal consistency without requiring metric destruction. This model suggests that the stress-energy tensor remains bounded, allowing for stable, non-paradoxical traversability of Cauchy horizons by macroscopic entities.