Regge pole description of scattering of gravitational waves by a Schwarzschild black hole

Abstract

We revisit the problem of plane monochromatic gravitational waves impinging upon a Schwarzschild black hole using complex angular momentum techniques. By extending our previous study concerning scalar and electromagnetic waves [A. Folacci and M. Ould El Hadj, Phys. Rev. D 99, 104079 (2019)PRVDAQ2470-001010.1103/PhysRevD.99.104079], we provide complex angular momentum representations and Regge pole approximations of the helicity-preserving and helicity-reversing scattering amplitudes and of the total differential scattering cross section. We show, in particular, that for high frequencies (i.e., in the short-wavelength regime), a small number of Regge poles permits us to describe numerically with very good agreement the black-hole glory and the orbiting oscillations and we then provide a semiclassical approximation that unifies these two phenomena.