The gravitational Field of a massless Particle on the Horizon of a stationary Black Hole

TL;DR

This paper calculates the gravitational shockwave generated by a massless particle at the horizon of a Kerr-Newman black hole, providing an exact solution and extending previous static black hole results.

Contribution

It introduces a method to derive an exact shockwave solution on a rotating black hole horizon using generalized Kerr-Schild and Newman-Penrose formalisms.

Findings

Exact linear differential equation for the shockwave profile

Solution generalizes static black hole shockwaves to rotating cases

Physical interpretation of the shockwave spacetime

Abstract

In this work, the field of a gravitational shockwave generated by a massless point-like particle is calculated at the event horizon of a stationary Kerr-Newman black hole. Using the geometric framework of generalized Kerr-Schild deformations in combination with the spin-coefficient formalism of Newman and Penrose, it is shown that the field equations of the theory, at the event horizon of the black hole, can be reduced to a single linear ordinary differential equation for the so-called profile function of the geometry. This differential relation is solved exactly. Based on the results obtained, a physical interpretation is given for the found shockwave spacetime, and it is clarified how these results lead back to those of previous works on the subject, which deal with the much simpler cases of gravitational shockwaves in static black hole backgrounds.