Polarisation Singularities of Gravitational Waves

TL;DR

This paper extends the concept of polarisation singularities from electromagnetic waves to gravitational waves, revealing their generic presence and dependence on the field's spin, supported by simulations and analysis.

Contribution

It introduces the theory of polarisation singularities for gravitational waves and higher spin fields, showing their generic occurrence and dependence on spin.

Findings

Polarisation singularities are common in gravitational waves.

Their dimension varies with the spin of the field.

Simulations demonstrate the density and structure of these singularities.

Abstract

Departure from idealised plane waves gives rise to intricate geometric structures in wave fields. One such structure is the polarisation singularity, which emerges when multiple monochromatic waves interfere (such as would be the case for stochastic backgrounds), producing loci of purely circular or linear polarisation. In this work, we extend the theory of polarisation singularities to gravitational waves and higher spin fields. Building on the electromagnetic description, we formulate the gravitational analogue of polarisation singularities and show that they are generic features of gravitational waves. Their dimension, however, depends on the spin of the field. We illustrate these results with simulations of plane-wave interference and analyse the resulting singularity densities.