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 non-special conformal Killing vectors are determined. It is shown that non-flat 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 non-Einstein-vacuum pp-wave with a proper special conformal Killing vector, and a non-conformally-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 vectors are explicitly determined.