Analytic Solution for the Motion of Spinning Particles in Kerr Space-Time
arXiv:2411.16855 · doi:10.1103/PhysRevLett.134.171401
Abstract
The equations of motion of massive test particles near Kerr black holes are separable in Boyer-Lindquist coordinates, as established by Carter. This separability, however, is lost when the particles are endowed with classical spin. We show that separability of the equations of motion can be recovered to linear order in spin by a shift of the worldline derived with the use of the hidden symmetry of Kerr space-time. Consequently, the closed-form solution of the motion is expressed in a way closely analogous to the solution for spinless particles. This finding enriches the understanding of separability and integrability properties of the dynamics of test particles and fields in Kerr space-time and is particularly valuable for modeling inspirals of rotating compact objects into massive black holes.
Supplemental Mathematica notebook available
References in corpus (27)
- TianQin: a space-borne gravitational wave detector
- The motion of point particles in curved spacetime
- Science with the space-based interferometer LISA. V: Extreme mass-ratio inspirals
- Taiji Program: Gravitational-Wave Sources
- Perturbative Approach to an orbital evolution around a Supermassive black hole
- New Horizons for Fundamental Physics with LISA
- Using LISA EMRI sources to test off-Kerr deviations in the geometry of massive black holes
- SUSY in the sky
- Spinning Black Hole Binary Dynamics, Scattering Amplitudes and Effective Field Theory
- An improved effective-one-body Hamiltonian for spinning black-hole binaries
- Black holes, hidden symmetries, and complete integrability
- Analytical solutions of bound timelike geodesic orbits in Kerr spacetime
- A new effective-one-body description of coalescing nonprecessing spinning black-hole binaries
- Gravitational Bremsstrahlung and Hidden Supersymmetry of Spinning Bodies
- The location of the last stable orbit in Kerr spacetime
- Canonical Hamiltonian for an extended test body in curved spacetime: To quadratic order in spin
- Adiabatic radiation reaction to the orbits in Kerr Spacetime
- Analytic solutions for parallel transport along generic bound geodesics in Kerr spacetime
- Hamilton-Jacobi equation for spinning particles near black holes
- Hamiltonians and canonical coordinates for spinning particles in curved space-time
- On Integrability of spinning particle motion in higher-dimensional black hole spacetimes
- Analytic solutions for the motion of spinning particles near spherically symmetric black holes and exotic compact objects
- Kerr Geodesics in Terms of Weierstrass Elliptic Functions
- Spinning particles near Kerr black holes: Orbits and gravitational-wave fluxes through the Hamilton-Jacobi formalism
- Generalized Carter constant for quadrupolar test bodies in Kerr spacetime
- 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
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- Dynamics of spinning particles in Reissner-Nordström black hole exterior
- Post-adiabatic waveform-generation framework for asymmetric precessing binaries
- Circular equatorial orbits of extended bodies with spin-induced quadrupole around a Kerr black hole: Comparing spin-supplementary conditions
- The spinning self-force EFT: 1SF waveform recursion relation and Compton scattering
- Black hole photon ring beyond General Relativity: an integrable parametrization
- Secondary spins of extreme mass ratio inspirals: A probe to the formation channels
- Conserved quantities and integrability for massless spinning particles in general relativity
- Spherical inspirals of spinning bodies into Kerr black holes
- 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