Kundt gravitational waves coupled with a non-Noetherian conformal scalar field

Type N spacetimes of the Kundt class are presented as solutions to Einstein's equations sourced by a real scalar field whose equation of motion is conformally invariant and that generalizes the standard conformal scalar field. The specific spacetimes considered model gravitational waves with uniform and totally geodesic wave fronts, propagating in a maximally symmetric background, and are characterized by the value of their constant scalar curvature and by the so-called wave profile function. All subclasses of such spacetimes are analyzed. It is shown that the scalar field solutions generically divide into two branches, of which one has a strikingly different behavior from that of the standard conformal case. The scalar field contributes to the equation satisfied by the wave profile function by adding new singular terms. Closed form and mode solutions for the wave profile function are found for different scenarios. The resulting energy-momentum tensor has a null eigenvector, but is more general than the pure radiation type usually coupled with this kind of spacetimes.