Completing the Fifth PN Precision Frontier via the EFT of Spinning Gravitating Objects

Authors: Michèle Levi, Zhewei Yin

Preprint number: UUITP-54/22

We derive and establish the new precision frontier at the fifth PN (5PN) order, and put forward a broader picture of the effective theory of a spinning particle within the EFT of spinning gravitating objects. This precision frontier includes higher-spin sectors, quadratic and quartic in the spin, which both display novel physical effects, from the extension of the effective theory beyond linear order in the curvature. In the quadratic-in-spin sectors there is a new tidal effect, and in the quartic-in-spin sectors there is a new multipolar deformation. With eyes towards the next precision frontier, we then generalize the concept of tidal operators and of spin-induced multipolar deformations, and make conjectures on the numerical values of their Wilson coefficients for Kerr black holes. We confirm the generalized actions for generic compact objects of the NLO quartic-in-spin sectors which were derived via the extension of the EFT of gravitating spinning objects. We derive the consequent interaction potentials and general Hamiltonians, that consist of 12 distinct sectors, with a new one due to the new multipolar deformation. These Hamiltonians give the full information on the binary system, which partly gets lost, especially in higher-spin sectors, when going to observables with aligned-spins, since generic spin orientations have an observational signature in the gravitational waveform. Moreover with these Hamiltonians, obtained within our framework, we find the complete Poincaré algebra at the 5PN order with spins. We derive observables for GW applications, and to further make contact with the scattering problem, we also derive the extrapolated scattering angles with aligned spins. The completion of the Poincaré algebra provides the strongest validation to our most comprehensive new results, and thus that the 5PN order has now been established as the new precision frontier.