Kundt spacetimes in the Einstein-Gauss-Bonnet theory

TL;DR

This paper classifies and analyzes Kundt vacuum solutions in Einstein-Gauss-Bonnet gravity, revealing new gravitational wave features not present in general relativity.

Contribution

It provides a systematic classification of Kundt solutions in Einstein-Gauss-Bonnet theory and explores their unique properties and explicit examples.

Findings

Classified Kundt solutions into three subfamilies.

Derived explicit curvature tensor structures and scalars.

Identified novel gravitational wave features in EGB theory.

Abstract

We systematically investigate the complete class of vacuum solutions in the Einstein-Gauss-Bonnet gravity theory which belong to the Kundt family of non-expanding, shear-free and twist-free geometries (without gyratonic matter terms) in any dimension. The field equations are explicitly derived and simplified, and their solutions classified into three distinct subfamilies. Algebraic structures of the Weyl and Ricci curvature tensors are determined. The corresponding curvature scalars directly enter the invariant form of equation of geodesic deviation, enabling us to understand the specific local physical properties of the gravitational field constrained by the EGB theory. We also present and analyze several interesting explicit classes of such vacuum solutions, namely the Ricci type III spacetimes, all geometries with constant-curvature transverse space, and the whole pp-wave class admitting a covariantly constant null vector field. These exact Kundt EGB gravitational waves exhibit new features which are not possible in Einstein's general relativity.