Scale-Dependent Conformal Coupling: Suppression of Proper-Time Accumulation in Divergent Curvature Regimes

This paper was originally published on Zenodo (DOI: https://doi.org/10.5281/zenodo.18131818 ). I am sharing it here on Figshare to encourage community feedback and discussion.This paper explores an effective phenomenological approach to address the challenge of physical singularities in General Relativity (GR). We propose a modified Einstein-Hilbert action incorporating a curvature-invariant-dependent conformal coupling, where the physical metric \tilde{g}_{\mu\nu} is modulated by a conformal factor \Omega^{2}(\mathcal{I}) linked to the Kretschmann scalar \mathcal{I}. The functional form of this coupling is designed such that as curvature approaches the Planck scale and diverges (\mathcal{I} \rightarrow \infty), the conformal factor vanishes (\Omega \rightarrow 0). Our results demonstrate a "temporal freezing" effect, characterized by the suppression of proper-time accumulation (d\tau = \Omega(\mathcal{I})d\tau_{GR}) for test particles in extreme gravity regimes. While the background geometric singularity may persist, this framework effectively regularizes the event from a physical perspective by ensuring that an infalling observer never reaches the singularity in finite proper time. The model maintains causal invariance and remains consistent with current gravitational redshift observations for neutron stars. This study provides a mathematically defensible bridge for understanding regimes where classical temporal flow ceases to accumulate. I am actively looking for feedback on the mathematical consistency of the conformal factor and the physical implications of temporal freezing. Please leave your thoughts in the comments section below!