On the integrability of extended test body dynamics around black holes

Abstract

In general relativity, the motion of an extended test body is influenced by its proper rotation, or spin. We present a covariant and physically self-consistent Hamiltonian framework to study this motion, up to quadratic order in the body's spin, including a spin-induced quadrupole, and in an arbitrary background spacetime. The choice of spin supplementary condition and degeneracies associated with local Lorentz invariance are treated rigorously with adapted tools from Hamiltonian mechanics. Applying the formalism to a background space-time described by the Kerr metric, we prove that the motion of any test compact object around a rotating black hole defines an integrable Hamiltonian system to linear order in the body's spin. Moreover, this integrability still holds at quadratic order in spin when the compact object has the deformability expected for an isolated black hole. Our analytical results shed light on longstanding numerical conjectures regarding spin-induced chaos in the motion of asymmetric compact binaries, and provides a powerful framework to improve current gravitational waveform modelling to account for spin-induced extended body effects.

6 pages, coincides with published version

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Cited by in corpus (10)

• Analytic Solution for the Motion of Spinning Particles in Kerr Space-Time
• Post-adiabatic waveform-generation framework for asymmetric precessing binaries
• Black hole photon ring beyond General Relativity: an integrable parametrization
• The spinning self-force EFT: 1SF waveform recursion relation and Compton scattering
• Symplectic mechanics of relativistic spinning compact bodies II.: Canonical formalism in the Schwarzschild spacetime
• Conserved quantities and integrability for massless spinning particles in general relativity
• Constants of motion in gravitational self-force theory
• Unexpected Symmetries of Kerr Black Hole Scattering
• Particles with precessing spin in Kerr spacetime: analytic solutions for eccentric orbits and homoclinic motion near the equatorial plane
• Spinning test particles in the spacetime of a global monopole