Null geodesics and wave front singularities in the Gödel space–time

Abstract

We explore wave fronts of null geodesics in the Gödel 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 Gödel 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.PACS 95.30.Sf, 04.90.+e, 04.20.Gz

Wave Fronts in a Causality-Violating Gödel-Type Metric

“…The threedimensional wave front plots were created using the Walnut package created by Eric Grotzke. Light ray and wave front diagrams for the Gödel space-time were originally reported in a paper by Kling et al [25].…”

“…Similar to the case in the Type D metric, the mathematics indicates that the observer at the origin would consider the pulse emitted at x a p to undergo the same type of behavior as described above, as is shown in Figure 2. However, both the blue sky appearance and the annihilation of the pulse pairs occur outside the causal boundary for an observer at the origin, hiding much of the odd behavior [25].…”

Wave Fronts in a Causality Violating Godel-Type Metric

“…3. However, both the blue-sky appearance and the annihilation of the pulse pairs occurs outside the causal boundary for an observer at the origin, hiding much of the odd behavior [21].…”

“…The three-dimensional wave fronts plots were created using the Walnut package create by Eric Grotzke. Light ray and wave front diagrams for the Gödel space-time were originally reported in a paper by Thomas Kling, Kevin Roebuck, and Eric Grotzke [21].…”