Trautman Problem and its Solution for Plane Waves in Riemann and Riemann–Cartan Spaces

The Trautman problem determines the conditions under which GWs transfer the information contained in them in an invariant manner. According to the analogy between plane gravitational and electromagnetic waves, the metric tensor of a plane gravitational wave is invariant under the five-dimensional group \(G_{5}\), which does not change the null hypersurface of the plane wave front. The theorems are proven on the equality to zero for the result of the action of the Lie derivative on the curvature 2-form of a plane GW in Riemann and Riemann–Cartan spaces in the direction determined by the vector generating the group \(G_{5}\). Thus the curvature tensor of a plane gravitational wave can invariantly transfer the information encoded in the source of the GW.