Null Geodesics and Wave Front Singularities in the Godel Space-time

TL;DR

This paper investigates the behavior of null geodesic wave fronts in Godel spacetime, revealing cusp formations, blue sky metamorphoses, and the impact of a new physical distance measure on wave front singularities.

Contribution

It introduces the concept of physical distance along null geodesics and analyzes how it affects wave front singularities in Godel spacetime.

Findings

Identification of cusp ridges and blue sky metamorphoses in wave fronts.

Blue sky metamorphoses demonstrate non-causal features of Godel spacetime.

Using physical distance removes cusp ridges from wave front reorganizations.

Abstract

We explore wave fronts of null geodesics in the Godel metric emitted from point sources both at, and away from, the origin. For constant time wave fronts emitted by sources away from the origin, we find cusp ridges as well as blue sky metamorphoses where spatially disconnected portions of the wave front appear, connect to the main wave front, and then later break free and vanish. These blue sky metamorphoses in the constant time wave fronts highlight the non-causal features of the Godel metric. We introduce a concept of physical distance along the null geodesics, and show that for wave fronts of constant physical distance, the reorganization of the points making up the wave front leads to the removal of cusp ridges.