of mutually stationary test particles in flat (Minkowski) spacetime. With respect to the timelike geodesic congruence of world lines obtained by integrating the timelike unit vector field , the expansion tensor shows that our test particles are expanding or contracting isotropically and transversely to the direction of propagation. This is exactly what we would expect for a transverse spin-0 wave; the behavior of analogous families of test particles which encounter a gravitational plane wave in general relativity is quite different, because these are spin-2 waves. This is due to the fact that Nordström's theory of gravitation is a scalar theory, whereas Einstein's theory of gravitation (general relativity) is a tensor theory. On the other hand, gravitational waves in both theories are transverse waves. Electromagnetic plane waves are of course also transverse. The tidal tensor further exhibits the spin-0 character of the gravitational plane wave in Nordström's theory. (The tidal tensor and expansion tensor are three-dimensional tensors which "live" in the hyperplane elements orthogonal to , which in this case happens to be irrotational, so we can regard these tensors as defined on orthogonal hyperslices.) The exact solution we are discussing here, which we interpret as a propagating gravitational plane wave, gives some basic insight into the propagation of gravitational radiation in Nordström's theory, but it does not yield any insight into the generation of gravitational radiation in this theory. At this point, it would be natural to discuss the analog for Nordström's theory of gravitation of the standard linearized gravitational wave theory in general relativity, but we shall not pursue this. See also Classical theories of gravitation Congruence (general relativity) Gunnar Nordström Obsolete physical theories General Theory of Relativity References Ravndal, Finn (2004). Scalar Gravitation and Extra Dimensions See problem 13.2. Theories of gravity Obsolete theories in physics