Visualizing gravitational Bessel waves

TL;DR

This paper derives and visualizes a gravitational vortex wave solution in four-dimensional spacetime, revealing its polarization and topological features through tendex and vortex line analysis.

Contribution

It introduces a new explicit vortex-inspired gravitational wave solution in 4D and visualizes its spacetime perturbations using tendex and vortex lines.

Findings

The solution exhibits a rotating polarization pattern.

Tendex and vortex line visualizations reveal the wave's topological structure.

The quadrupolelike case shows characteristic wave features.

Abstract

We explicitly derive a~vortex inspired solution for the metric perturbation within the linearized Einsteins general theory of relativity in arbitrary dimensions $D\geq 4$. We focus on $D=4$ where our solution is the gravitational analog of the well-known electromagnetic (or electron) Bessel vortex beams. Next we visualize the perturbed spacetime via tidal tendexes and frame-drag vortexes. We display and analyze mostly two-dimensional sections of the tendexes and the vortexes for different values of an angular momentum of the wave solution. Corresponding geodesic deviation equations are solved and the results are visualized. We show that the physically most important quadrupolelike case leads to a~wave with rotating polarization. We discuss asymptotical features of the found solution. We provide also several 3D plots of tendex lines. One of them concerns a~special cylindrical-like case and we utilize the topological classification of singularities of the depicted line fields as an approach to characterize the radiation field.