We provide a detailed and rigorous proof of (a generalized version of) the Ehlers-Geroch theorem on geodesic motion in metric theories of gravity: we assume that (M, g) is a spacetime satisfying an averaged form of the dominant energy condition and some further technical assumptions indicated in the bulk of this paper. Then, a small body which is allowed to deform the original spacetime metric g moves, nonetheless, along a geodesic of (M, g).

[6]. In this paper we address the issue of wave propagation about a static Hopf soliton in the context of the Nicole model. Working within the geometrical optics limit we show that several nontrivial lensing effects emerge due to nonlinear interactions as long as the theory remains hyperbolic. We conclude that similar effects are very likely to occur in effective field theories characterized by a topological invariant such as the Skyrme model of pions.