# Approaching a spacetime singularity in conformal gravity

## TL;DR

This paper demonstrates that Kasner spacetime, traditionally singular in general relativity, becomes regular and free of singularities within Einstein's conformal gravity, ensuring geodesic completeness for various particles.

## Contribution

It shows that Kasner spacetime is nonsingular in Einstein's conformal gravity, highlighting the regularity of curvature invariants and geodesic completeness.

## Key findings

- Kasner spacetime is singularity-free in conformal gravity.
- Curvature invariants remain regular at the former singularity.
- Spacetime is geodesically complete for all particle types.

## Abstract

We hereby show that the Kasner spacetime turns out to be singularity-free in Einstein's conformal gravity in vacuum or in presence of matter. Such a statement is based on the regularity of the curvature invariants and on the geodesic completion of the spacetime when it is probed by massive, massless, and conformally coupled particles. As a universal feature of the regular metric, nothing can reach the singularity located in t=0 in a finite amount of proper time (for massive particles and conformally coupled particles) or for finite values of the affine parameter (for massless particles).