# Gravitational shockwaves on rotating black holes

## TL;DR

This paper derives an exact solution describing gravitational shockwaves caused by a massless particle on the horizon of a rotating black hole, revealing insights into nonlinear effects in such extreme spacetime conditions.

## Contribution

It provides a new exact solution for gravitational shockwaves on Kerr-Newman black holes using advanced formalisms, highlighting conditions where nonlinearities vanish.

## Key findings

- Exact shockwave solution on Kerr-Newman horizon
- Nonlinearities in curvature scalars can vanish under specific conditions
- Utilizes spin coefficient formalism for solution derivation

## Abstract

We present an exact solution of Einstein's equation that describes the gravitational shockwave of a massless particle on the horizon of a Kerr-Newman black hole. The backreacted metric is of the generalized Kerr-Schild form and is Type II in the Petrov classification. We show that if the background frame is aligned with shear-free null geodesics, and if the background Ricci tensor satisfies a simple condition, then all nonlinearities in the perturbation will drop out of the curvature scalars. We make heavy use of the method of spin coefficients (the Newman-Penrose formalism) in its compacted form (the Geroch-Held-Penrose formalism).