Geodesic deviation in Kundt spacetimes of any dimension

Abstract

Using the invariant form of the equation of geodesic deviation, which describes relative motion of free test particles, we investigate a general family of D-dimensional Kundt spacetimes. We demonstrate that local influence of the gravitational field can be naturally decomposed into Newton-type tidal effects typical for type II spacetimes, longitudinal deformations mainly present in spacetimes of algebraic type III, and type N purely transverse effects corresponding to gravitational waves with D(D-3)/2 independent polarization states. We explicitly study the most important examples, namely exact pp-waves, gyratons, and VSI spacetimes. This analysis helps us to clarify the geometrical and physical interpretation of the Kundt class of nonexpanding, nontwisting and shearfree geometries.