From the EFT of Spinning Gravitating Objects to Poincaré and Gauge Invariance
Authors: Michèle Levi, Roger Morales, Zhewei Yin
Preprint number: UUITP-48/22
In this paper we confirm the generalized actions of the complete NLO cubic-in-spin interactions for generic compact objects which were tackled first via an extension of the EFT of spinning gravitating objects. The interaction potentials are made up of 6 independent sectors, including a new unique sector that is proportional to the square of the quadrupolar deformation parameter, CES2. We derived the full Hamiltonians in an arbitrary reference frame and in generic kinematic configurations. Using these most general Hamiltonians we find the full Poincaré algebra of all the sectors at the 4.5PN order, including the third subleading spin-orbit sector recently derived within our approach. We also derive the binding energies with gauge-invariant relations useful for gravitational-wave applications. Finally, we derive the extrapolated scattering angles in the aligned-spins case, and we find complete agreement with previous results derived for the scattering of black holes via scattering-amplitudes methods. The completion of the full Poincaré algebra at the 4.5PN order provides a strong validation that this new precision frontier in PN theory has now been established.