On Singularity Free Spacetimes--II : mid Geodesic Completeness

TL;DR

This paper proves that a specific singularity-free spacetime metric is geodesically complete, globally hyperbolic, and causally stable, thereby demonstrating the absence of singularities without relying on particular matter distributions.

Contribution

It establishes geodesic completeness and causal stability for a singularity-free spacetime metric, extending previous work and discussing implications for singularity theorems.

Findings

The metric is geodesically complete.

The spacetime is globally hyperbolic.

Singularity theorems do not apply in this case.

Abstract

We study the geodesics of the singularity free metric considered in the preceding Paper I and show that they are complete. This once again demonstrates the absence of singularity. The geodesic completeness is established in general without reference to any particular matter distribution. The metric is globally hyperbolic and causally stable. The question of inapplicability of the powerful singularity theorems in this case is discussed.