Motion of charged particles in a NUTty Einstein-Maxwell spacetime and causality violation

TL;DR

This paper studies the motion of charged particles in NUTty Einstein-Maxwell spacetimes with closed timelike curves, showing causality is preserved for distant observers despite the presence of potential well worldlines.

Contribution

It demonstrates that in certain NUTty spacetimes, causality remains intact for charged particles moving under Lorentz force, despite closed timelike curves.

Findings

Closed worldlines exist inside potential wells in wormhole cases.

Distant charged observers' worldlines do not close or self-intersect.

Causality is preserved for these observers, supporting weak chronology protection.

Abstract

We investigate the motion of electrically charged test particles in spacetimes with closed timelike curves, a subset of the black hole or wormhole Reissner-Nordstr\"om-NUT spacetimes without periodic identification of time. We show that, while in the wormhole case there are closed worldlines inside a potential well, the wordlines of initially distant charged observers moving under the action of the Lorentz force can never close or self-intersect. This means that for these observers causality is preserved, which is an instance of our weak chronology protection criterion.