Geodesics in the static Mallett spacetime

TL;DR

This paper analyzes the static Mallett spacetime, revealing that while some null geodesics escape, all timelike geodesics originate and end at the singularity, with matter being destroyed upon reaching it.

Contribution

It provides a detailed analysis of the geodesic structure in the static Mallett spacetime, clarifying the behavior of matter and light in this geometry.

Findings

Some null geodesics escape to infinity.

All timelike geodesics originate and terminate at the singularity.

Freely falling matter is destroyed at the singularity.

Abstract

Mallett has exhibited a cylindrically symmetric spacetime containing closed timelike curves produced by a light beam circulating around a line singularity. I analyze the static version of this spacetime obtained by setting the intensity of the light to zero. Some null geodesics can escape to infinity, but all timelike geodesics in this spacetime originate and terminate at the singularity. Freely falling matter originally at rest quickly attains relativistic velocity inward and is destroyed at the singularity.