Geodesic Completeness of Orthogonally Transitive Cylindrical Spacetimes

TL;DR

This paper establishes a sufficient condition for orthogonally transitive cylindrical spacetimes to be free of singularities, and tests this condition on known regular curvature invariant examples.

Contribution

It introduces a new theorem providing a broad criterion for singularity-free cylindrical spacetimes and verifies its applicability on existing literature examples.

Findings

The theorem successfully identifies singularity-free spacetimes.

Examples from literature satisfy the theorem's conditions.

The approach broadens understanding of spacetime regularity.

Abstract

In this paper a theorem is derived in order to provide a wide sufficient condition for an orthogonally transitive cylindrical spacetime to be singularity-free. The applicability of the theorem is tested on examples provided by the literature that are known to have regular curvature invariants.