A remark on kinks and time machines

TL;DR

This paper provides a simple proof that certain topological manifolds resembling the Politzer time machine cannot support a smooth, flat Lorentzian metric without singularities.

Contribution

It offers an elementary proof demonstrating the incompatibility of the Politzer time machine topology with nonsingular, asymptotically flat Lorentz metrics.

Findings

Manifolds with Politzer topology cannot admit nonsingular Lorentz metrics.

The proof is elementary and straightforward.

The result constrains possible spacetime geometries with such topologies.

Abstract

We describe an elementary proof that a manifold with the topology of the Politzer time machine does not admit a nonsingular, asymptotically flat Lorentz metric.