A NOTE ON THE SYMMETRIES OF THE GRAVITATIONAL-FIELD OF A MASSLESS PARTICLE

It is shown that the metric of a massless particle obtained from boosting the Schwarzschild metric to the velocity of light, has four Killing vectors corresponding to an E(2) x R symmetry group. This is in agreement with the expectations based on flat-space kinematics but is in contrast to previous statements in the literature (Schucker). Moreover, it also goes beyond the general Jordan-Ehlers-Kundt (JEK) classification of gravitational pp-waves as given by Ehlers and Kundt.