Abstract
The Kundt class is geometrically defined to admit a null geodesic congruence with a vanishing expansion, shear, and twist. In our contribution we analyse these geometries in specific higher-order extensions of Einstein's general relativity.
In particular, we focus on theories with action containing additional terms quadratic in the Riemann tensor and its contractions. The corresponding field equations are thus in general of the fourth order.
We study their restrictions imposed on the Kundt geometric ansatz and compare the results with those well-known in classic general relativity. In detail we discuss specific key model solutions, such as pp-waves or direct product spacetimes.
In order to provide means of physical interpretation of gravitational field, we investigate relative motion of a set of freely falling test particles.