Pc. Aichelburg et H. Balasin, A NOTE ON THE SYMMETRIES OF THE GRAVITATIONAL-FIELD OF A MASSLESS PARTICLE, Classical and quantum gravity, 11(10), 1994, pp. 121-123
It is shown that the metric of a massless particle obtained from boost
ing the Schwarzschild metric to the velocity of light, has four Killin
g vectors corresponding to an E(2) x R symmetry group. This is in agre
ement with the expectations based on flat-space kinematics but is in c
ontrast to previous statements in the literature (Schucker). Moreover,
it also goes beyond the general Jordan-Ehlers-Kundt (JEK) classificat
ion of gravitational pp-waves as given by Ehlers and Kundt.