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

## TL;DR

This paper applies complex angular momentum techniques to analyze gravitational wave scattering by a Schwarzschild black hole, providing Regge pole approximations that accurately describe scattering phenomena in the high-frequency regime.

## Contribution

It extends previous work on scalar and electromagnetic waves to gravitational waves, offering new Regge pole representations and semiclassical approximations for scattering amplitudes.

## Key findings

- Few Regge poles suffice to accurately describe glory and orbiting oscillations.
- High-frequency regime allows for effective semiclassical approximation.
- Regge pole method unifies different scattering phenomena.

## 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 {\bf 99}, 104079, (2019), arXiv:1901.03965], 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.