Closed timelike curves and geodesics of Godel-type metrics

TL;DR

This paper demonstrates the existence of closed timelike or null curves in Godel-type spacetimes when the characteristic vector is a Killing vector, and explores geodesic properties through Lorentz force equations with specific examples.

Contribution

It establishes conditions for closed timelike/null curves in Godel-type metrics and links geodesics to Lorentz force equations, providing explicit examples where geodesics are not closed.

Findings

Closed timelike/null curves exist when the characteristic vector is a Killing vector.

Geodesics are characterized by a Lorentz force equation in a Riemannian background.

Explicit examples show geodesics can be non-closed, even in Godel-type spacetimes.

Abstract

It is shown explicitly that when the characteristic vector field that defines a Godel-type metric is also a Killing vector, there always exist closed timelike or null curves in spacetimes described by such a metric. For these geometries, the geodesic curves are also shown to be characterized by a lower dimensional Lorentz force equation for a charged point particle in the relevant Riemannian background. Moreover, two explicit examples are given for which timelike and null geodesics can never be closed.