Scattering in black hole backgrounds and higher-spin amplitudes. Part I
Yilber Bautista (Perimeter Institute for Theoretical Physics, Waterloo, ON, N2L 2Y5, Canada, Department of Physics and Astronomy, York University, Toronto, Ontario, M3J 1P3, Canada); Alfredo Guevara (Perimeter Institute for Theoretical Physics, Waterloo, ON, N2L 2Y5, Canada, Society of Fellows, Harvard University, Cambridge, MA, 02138, USA); Chris Kavanagh (Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, Potsdam, 14476, Germany); Justin Vines (Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, Potsdam, 14476, Germany)
The scattering of massless waves of helicity $$ \mid h\mid =0,\frac{1}{2},1 $$ in Schwarzschild and Kerr backgrounds is revisited in the long-wavelength regime. Using a novel description of such backgrounds in terms of gravitating massive particles, we compute classical wave scattering in terms of 2 → 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.
