A worldsheet for Kerr

TL;DR

This work reframes the Newman-Janis shift of the Kerr solution as a two-dimensional worldsheet effective action sourced by the spin of a particle, a structure that persists into the leading interactions of Kerr and its electromagnetic single-copy, sqrt(Kerr). By matching three-point amplitudes in split signature to a worldsheet EFT, it derives translation operators that realize the shift and yields a covariant worldsheet action whose boundary and bulk terms encode the NJ phenomenon. The framework uses spinor-helicity methods to produce chiral, classical equations of motion for both electromagnetic and gravitational cases, facilitating calculation of impulses and angular impulses in Kerr–Kerr and Kerr–Taub–NUT scattering. It also shows how the worldsheet naturally reproduces the standard spin–curvature interactions via a tower of single-Riemann operators and extends to the gravitational double copy, offering a geometric foundation for Kerr dynamics with potential constraints on higher-dimension operators.

Abstract

We show that the Newman-Janis shift property of the exact Kerr solution can be interpreted in terms of a worldsheet effective action. This holds both in gravity, and for the single-copy $\sqrt{\text{Kerr}}$ solution in electrodynamics. At the level of equations of motion, we show that the Newman-Janis shift holds also for the leading interactions of the Kerr black hole. These leading interactions are conveniently described using chiral classical equations of motion with the help of the spinor-helicity method familiar from scattering amplitudes.

Figures (1)

• Figure 1: Geometry of the effective action: boundary $\partial \Sigma_\text{n}$ of the complex worldsheet (translucent plane) is fixed to the particle worldline in real space (solid plane).