Gravitational Shock Waves for Schwarzschild and Kerr Black Holes

TL;DR

This paper derives metrics for gravitational shock waves in Schwarzschild and Kerr black holes, analyzing their properties and potential astrophysical applications.

Contribution

It provides new explicit metrics for shock waves in Schwarzschild and Kerr black holes, including cases with black hole motion and coordinate effects.

Findings

Derived shock wave metrics for Schwarzschild and Kerr black holes

Analyzed null coordinate shifts and refraction angles across shock waves

Discussed potential astrophysical implications

Abstract

The metrics of gravitational shock waves for a Schwarzschild black hole in ordinary 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 discussed in short.