Unexpected Symmetries of Kerr Black Hole Scattering

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 Rüdiger 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.

13 pages, 5 tables, includes ancillary file for the radial action at various orders of G and spin

References in corpus (43)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Two timescale analysis of extreme mass ratio inspirals in Kerr. I. Orbital Motion
• Scattering Amplitudes, the Tail Effect, and Conservative Binary Dynamics at $O(G^4)$
• Dynamics of Binary Systems to Fourth Post-Minkowskian Order from the Effective Field Theory Approach
• Gravitational Bremsstrahlung and Hidden Supersymmetry of Spinning Bodies
• Spin Effects in the Effective Field Theory Approach to Post-Minkowskian Conservative Dynamics
• Quadratic-in-Spin Hamiltonian at $\mathcal{O}(G^2)$ from Scattering Amplitudes
• Radiation-Reaction in the Effective Field Theory Approach to Post-Minkowskian Dynamics
• Conservative and radiative dynamics of spinning bodies at third post-Minkowskian order using worldline quantum field theory
• Binary Dynamics Through the Fifth Power of Spin at $\mathcal{O}(G^2)$
• A worldsheet for Kerr
• Classical gravitational spinning-spinless scattering at $\mathcal{O}(G^2{S}^{\infty })$
• Gravitational spin-orbit coupling in binary systems, post-Minkowskian approximation and effective one-body theory
• The 2PM Hamiltonian for binary Kerr to quartic in spin
• Conservative Binary Dynamics with a Spinning Black Hole at $\mathcal{O}(G^3)$ from Scattering Amplitudes
• Emergence of Calabi-Yau manifolds in high-precision black hole scattering
• Resummed spinning waveforms from five-point amplitudes
• Linear Response, Hamiltonian and Radiative Spinning Two-Body Dynamics
• Listening to the Universe with Next Generation Ground-Based Gravitational-Wave Detectors
• Scattering Angles in Kerr Metrics
• Spinning waveforms from KMOC at leading order
• Classical gravitational scattering at $\mathcal{O}(G^2{S}_1^{\infty }{S}_2^{\infty })$
• Boundary to bound dictionary for generic Kerr orbits
• Scattering and bound observables for spinning particles in Kerr spacetime with generic spin orientations
• Observables from the Spinning Eikonal
• Integrability of eccentric, spinning black hole binaries up to second post-Newtonian order
• Complete set of quasi-conserved quantities for spinning particles around Kerr
• First Look at Quartic-in-Spin Binary Dynamics at Third Post-Minkowskian Order
• Spinning Black Hole Scattering at $\mathcal{O}(G^3{S}^2)$: Casimir Terms, Radial Action and Hidden Symmetry
• Generalized Carter constant for quadrupolar test bodies in Kerr spacetime
• Massive twistor worldline in electromagnetic fields
• Analytic Solution for the Motion of Spinning Particles in Kerr Space-Time
• Covariant actions and propagators for all spins, masses, and dimensions
• Radiation eikonal for post-Minkowskian observables
• Actions of spinning compact binaries: Spinning particle in Kerr matched to dynamics at 1.5 post-Newtonian order
• On the integrability of extended test body dynamics around black holes
• Bootstrapping spinning two body problem in dynamical Chern-Simons gravity using worldline QFT
• The spinning self-force EFT: 1SF waveform recursion relation and Compton scattering
• Dirac brackets for classical radiative observables
• Consistent actions for massive particles interacting with electromagnetism and gravity
• Symplectic mechanics of relativistic spinning compact bodies II.: Canonical formalism in the Schwarzschild spacetime
• Classical Observables using Exponentiated Spin factors: Electromagnetic Scattering