A Note on the Symmetries of the Gravitational Field of a Massless Particle
Abstract
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)× symmetry-group. This is in agreement with the expectations based on flat-space kinematics but is in contrast to previous statements in the literature Schueck. Moreover, it also goes beyond the general Jordan-Ehlers-Kundt-(JEK)-classification of gravitational pp-waves as given in JEK.
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