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2022

Linear Response, Hamiltonian and Radiative Spinning Two-Body Dynamics

Jakobsen, Gustav Uhre, Mogull, Gustav

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Using the spinning, supersymmetric Worldline Quantum Field Theory formalism we compute the momentum impulse and spin kick from a scattering of two spinning black holes or neutron stars up to quadratic order in spin at third post-Minkowskian (PM) order, including radiation-reaction effects and with arbitrarily mis-aligned spin directions.

Parts of these observables, both conservative and radiative, are also inferred from lower-PM scattering data by extending Bini and Damour's linear response formula to include mis-aligned spins.
By solving Hamilton's equations of motion we also use a conservative scattering angle to infer a complete 3PM two-body Hamiltonian including finite-size corrections and mis-aligned spin-spin interactions.
Finally, we describe mappings to the bound two-body dynamics for aligned spin vectors: including a numerical plot of the binding energy for circular orbits compared with numerical relativity, analytic confirmation of the NNLO PN binding energy and the energy loss over successive orbits.

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