What question did this study set out to answer?

This work aims to present a C ∞-smooth extension of classical relativity to address singularities.

March 30, 2026Open Access

Regularizing Relativistic Singularities through a C ∞ -Smooth Extension of the d'Alembert Invariance: Implications for the Hubble Tension

Key Points

This work aims to present a C ∞-smooth extension of classical relativity to address singularities.
Derived a C ∞-smooth extension replacing the divergent Lorentz factor.
Introduced the Asymptotic Lorentz Relativity (ALR) framework for singularity regularization.
Identified Hubble Matching Scale (HMS) for reconciling local SH0ES measurements with global constraints.
Demonstrated that the Hubble tension is an analytical residue of metric truncation.
Aligned the ALR framework with calls for a fundamental update to cosmological models.

Abstract

We derive a C^-smooth extension of classical relativity that regularizes singularities of SRT by replacing the divergent Lorentz factor with a structurally complete boost. Unlike the metric truncation inherent in Special Relativity, our Asymptotic Lorentz Relativity (ALR) framework provides the "missing information" necessary for a non-singular description of the high-energy regime. We demonstrate that the 5 Hubble tension is not a statistical anomaly but an analytical residue of this truncation. By restoring d'Alembertian form-invariance, we identify a Hubble Matching Scale (HMS) that reconciles local SH0ES measurements with global Planck constraints without auxiliary parameters. The framework aligns with recent calls for a fundamental update to the cosmological model (Binney et al. 2025) and addresses fundamental divergences in field theory (Leuchs & Sánchez-Soto 2025).

Regularizing Relativistic Singularities through a C ∞ -Smooth Extension of the d'Alembert Invariance: Implications for the Hubble Tension

Key Points

Abstract

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