The gravitational shock wave of a massless particle

Abstract

The (spherical) gravitational shock wave due to a massless particle moving at the speed of light along the horizon of the Schwarzchild black hole is obtained. Special cases of our procedure yield previous results by Aichelburg and Sexl[1] for a photon in Minkowski vpace and by Penrose [2] for sourceless shock waves in Minkowski space. A new derivation of the (plane) shock wave of a photon in Minkowski space [1] involving explicit calculation of geodesics crossing the shock wave is also given in order to clarify the underlying physics. Applications to quantum gravity, specifically the possible effect on the Hawking temperature, are briefly discussed.