Gravitational shock waves for Schwarzschild and Kerr black holes

Abstract

The metrics of gravitational shock waves for a Schwarzschild black hole in Schwarzschild coordinates and for a Kerr black hole in Boyer-Lindquist coordinates are derived. The Kerr metric is discussed for two cases: the case of a Kerr black hole moving parallel to the rotational axis, and moving perpendicular to the rotational axis. Then, two properties from the derived metrics are investigated: the shift of a null coordinate and the refraction angle crossing the gravitational shock wave. Astrophysical applications for these metrics are briefly discussed.