pp-waves in conformal Killing gravity

Recently Harada has proposed a gravitational theory which is of third order in the derivatives of the metric tensor. This has attracted some attention particularly as it predicts a late-time transition from cosmological decelaration to accelerated expansion without assuming the presence of dark energy or a non-zero cosmological constant. This theory has been dubbed conformal Killing gravity by Mantica & Molinari. The most general exact solutions of the Harada field equations are known for a number of important physical situations: homogeneous and isotropic cosmological models, static spherically symmetric vacuum and electrovac spacetimes. These are analogues of the well-known FRWL, Schwarzschild and Reissner-Nordstr\"om metrics of General Relativity(GR). In this study the pp-waves in Harada's theory are studied and the most general exact solution is obtained together with its specialisation for plane waves. The generalisation from GR to Harada's theory turns out to be straightforward and the solutions only involve an extra non-propagating term. The solutions have Petrov type N (or 0) and the Ricci tensor is either zero or the Segr\'e type is [(211)] with zero eigenvalue. For any metric in conformal Killing gravity it is shown that more than one possible matter source can generate the solution. If the metric admits one or more Killing vectors, the ambiguity in the possible matter sources increases.