Unexpected Symmetries of Kerr Black Hole Scattering

TL;DR

This paper explores conserved quantities and symmetries in Kerr black hole scattering using on-shell amplitude methods, revealing unexpected integrability properties and new insights into spin dynamics.

Contribution

It introduces a novel on-shell framework for analyzing conserved quantities and symmetries in Kerr black hole scattering, extending beyond the probe limit.

Findings

Conservation of energy, angular momentum, Rüdiger invariant, and Carter constant established up to third post-Minkowskian order.

New perspective on spin-shift symmetry clarifies its role in black hole dynamics.

Evidence of surprising asymptotic integrability for spinning probes in Kerr spacetime.

Abstract

Motivated by the recent introduction of the Dirac bracket framework to compute spinning observables for the scattering of Kerr black holes, we initiate the study of conserved quantities from an on-shell amplitude perspective. We establish new results for the conservation of energy, angular momentum, the R\"udiger invariant and the quadrupolar Carter constant using the spinning radial action extracted from the literature both in the probe limit and beyond, up to third post-Minkowskian order in the conservative sector. Furthermore, we offer a new perspective on the spin-shift symmetry of the radial action, clarifying its role in the dynamics. Finally, we define a new on-shell notion of asymptotic integrability in the Liouville sense and present strong evidence that it is surprisingly satisfied by a spinning probe in Kerr up to quartic order in the probe spin, to all orders in the post-Minkowskian expansion. We further establish integrability beyond the probe limit at low PM orders. Our results suggest important new implications for the dynamics of Kerr black holes.