Abstract
We systematically investigate the complete class of vacuum solutions in the Einstein-Gauss-Bonnet (EGB) gravity theory which belong to the Kundt family of nonexpanding, 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 the 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.