Item

Abstract

The scattering of massless waves of helicity $|h|=0,\frac{1}{2},1$ in
Schwarzschild and Kerr backgrounds is revisited in the long-wavelenght regime.
Using a novel description of such backgrounds in terms of gravitating massive
particles, we compute classical wave scattering in terms of $2\to 2$ QFT
amplitudes in flat space, to all orders in spin. The results are Newman-Penrose
amplitudes which are in direct correspondence with solutions of the
Regge-Wheeler/Teukolsky equation. By introducing a precise prescription for the
point-particle limit, in Part I of this work we show how both agree for $h=0$
at finite values of the scattering angle and arbitrary spin orientation.
Associated classical observables such as the scattering cross sections, wave
polarizations and time delay are studied at all orders in spin. The effect of
the black hole spin on the polarization and helicity of the waves is found in
agreement with previous analysis at linear order in spin. In the particular
limit of small scattering angle, we argue that wave scattering admits a
universal, point-particle description determined by the eikonal approximation.
We show how our results recover the scattering eikonal phase with spin up to
second post-Minkowskian order, and match it to the effective action of null
geodesics in a Kerr background. Using this correspondence we derive classical
observables such as polar and equatorial scattering angles.
This study serves as a preceding analysis to Part II, where the Gravitational
Wave ($h=2$) case will be studied in detail.