Note on the Kerr Spinning-Particle Equations of Motion

TL;DR

This paper introduces a novel method to derive spinning-particle equations of motion from Kerr black hole dynamics, revealing hidden symmetries and spin exponentiation in gravitational amplitudes.

Contribution

It develops a probe version of the Newman-Janis algorithm to connect geodesic deviation with exact spinning-particle equations, uncovering new symmetries in gravitational interactions.

Findings

Complete constraint of Kerr black hole dynamics in the self-dual sector.

Demonstration of spin exponentiation of same-helicity gravitational Compton amplitudes.

Identification of a hidden symmetry in the effective theory.

Abstract

We implement a probe counterpart of Newman-Janis algorithm, which Wick rotates the all-orders geodesic deviation equation into a part of exact spinning-particle equations of motion. Consequently, the gravitational dynamics of the Kerr black hole in its point-particle effective theory is completely constrained in the self-dual sector for a hidden symmetry, implying the spin exponentiation of same-helicity gravitational Compton amplitudes to all multiplicities.