Conformal symmetries of pp-waves

Previous results on Killing and special conformal Killing vectors of pp-waves are generalized by finding the general solution of the conformal Killing equations, together with integrability conditions. The general homothetic and nonspecial conformal Killing vectors are determined. It is shown that nonflat conformally flat pp-waves always admit a G₆ of motions and a G₁ of proper homothetic motions, but do not, in general, admit special conformal motions. Examples are given of a nonEinstein-vacuum pp-wave with a proper special conformal Killing vector, and a non-conformality-flat pp-wave with a non-special conformal Killing vector. A conformally flat pp-wave, which may be interpreted as an Einstein-Maxwell or Einstein-Klein-Gordon solution, is given and its fifteen conformal Killing vector are explicitly determined.