Inhomogeneous High Frequency Expansion-Free Gravitational Waves

TL;DR

This paper introduces a new class of inhomogeneous high frequency gravitational waves of the Kundt type, expanding the understanding of wave properties in general relativity, especially with non-constant propagation directions and cosmological constant effects.

Contribution

It presents a novel inhomogeneous generalization of high frequency gravitational waves with specific geometric properties and discusses the impact of a cosmological constant.

Findings

Inhomogeneous high frequency gravitational waves of Kundt type are characterized.

The null propagation direction has vanishing expansion, twist, and shear.

Comparison with wave fronts homeomorphic to 2-spheres is provided.

Abstract

We describe a natural inhomogeneous generalization of high frequency plane gravitational waves. The waves are high frequency waves of the Kundt type whose null propagation direction in space-time has vanishing expansion, twist and shear but is not covariantly constant. The introduction of a cosmological constant is discussed in some detail and a comparison is made with high frequency gravity waves having wave fronts homeomorphic to 2-spheres.