Higher Spinning Amplitudes from the Teukolsky Equation and Binary Kerr Observables

Abstract: Application of scattering amplitude techniques to address problems in classical gravity has become a practice of commune use in the last decade, this due to the remarkable correspondence between classical spin- ning black holes (BHs) and scattering amplitudes of massive spinning particles minimally couple to gravity. However, this correspondence has only been tested in few scenarios: in the static limit to all orders in the BH spin at the level of the 3-point amplitude, and in dynamic scenarios at third orders in spins, for the scattering of two Kerr BHs at second order in the post-Minkowskian (PM) expansion, indirectly proving the gravita- tional Compton amplitude. In this talk, we will test the correspondence at fourth order in spin, where minimally coupled amplitudes are well defined, by studding the scattering of waves of helicity h ≤ 2 off the Kerr BH, and extend the correspondence to higher orders in spins by extracting highers spin amplitudes from solutions of the Teukolsky equation. We will then illustrate how to use these higher spin amplitudes to compute observables for the binary Kerr problem at 2PM order, including the linear impulse and spin kicks for BHs whose spins have a generically orientation with respect to the angular momentum of the system.