Rehabilitating space-times with NUTs

TL;DR

This paper demonstrates that the Taub-NUT spacetime can be extended to a geodesically complete, singularity-free manifold without closed causal geodesics, challenging previous objections to its physical relevance.

Contribution

It shows that the Misner string is transparent for geodesics and that the spacetime can be analytically continued to remove singularities and obstructions.

Findings

Misner string is transparent for geodesics

Spacetime can be extended to be singularity-free

No closed causal geodesics despite CTC region

Abstract

We revisit the Taub-NUT solution of the Einstein equations without time periodicity condition, showing that the Misner string is still fully transparent for geodesics. In this case, analytic continuation can be carried out through both horizons leading to a Hausdorff spacetime without a central singularity, and thus geodesically complete. Furthermore, we show that, in spite of the presence of a region containing closed time-like curves, there are no closed causal {\em geodesics}. Thus, some longstanding obstructions to accept the Taub-NUT solution as physically relevant are removed.