The ultrarelativistic limit of Kerr

TL;DR

This paper investigates the ultrarelativistic limit of Kerr black holes, revealing that most candidate metrics lack spin effects at large distances, but one metric retains spin and finite size effects, with implications for scattering amplitudes.

Contribution

It introduces a novel analysis of the ultrarelativistic Kerr limit using Kerr-Schild impulsive pp-waves and connects metric profiles with scattering amplitudes, highlighting a unique metric with spin effects.

Findings

Most candidate metrics lack spin effects at large distances.

One specific metric retains spin and finite size effects at short distances.

The study links classical metrics with quantum scattering amplitudes.

Abstract

The massless (or ultrarelativistic) limit of a Schwarzschild black hole with fixed energy was determined long ago in the form of the Aichelburg-Sexl shockwave, but the status of the same limit for a Kerr black hole is less clear. In this paper, we explore the ultrarelativistic limit of Kerr in the class of Kerr-Schild impulsive pp-waves by exploiting a relation between the metric profile and the eikonal phase associated with scattering between a scalar and the source of the metric. This gives a map between candidate metrics and tree-level, 4-point scattering amplitudes. At large distances from the source, we find that all candidates for the massless limit of Kerr in this class do not have spin effects. This includes the metric corresponding to the massless limit of the amplitude for gravitational scattering between a scalar and a massive particle of infinite spin. One metric, discovered by Balasin and Nachbagauer, does have spin and finite size effects at short distances, leading to a remarkably compact scattering amplitude with many interesting properties. We also discuss the classical single copy of the ultrarelativistic limit of Kerr in electromagnetism.