On the gravitational scattering of gravitational waves

Abstract

We discuss the scattering of weak gravitational waves from a slowly rotating gravitational source, having mass M and angular momentum . We start considering the dynamics of a massless spin-2 field propagating in the weak gravitational field of the source, writing down the Fierz–Pauli in the presence of a slightly curved background. We adopt a semiclassical framework, where the gravitational background is described as a classical external field; meanwhile, the spin-2 field is treated quantum mechanically. In the weak-coupling limit, in which the typical wavelength of satisfies (where Rs is the Schwarzschild radius of the source), we obtain the cross-section for the scattering process in the Born approximation. We also discuss helicity asymmetry, showing its relationship with the spin-2 field coupling to the derivatives of the background metric. We finally consider the transition to the case of gravitational wave scattering, showing that—under reasonable assumptions—gravitational waves are expected to follow the same behavior. Our results partly agree with those presented through the years by various authors. The present analysis suggests that the scattering of weak gravitational waves in the field of a macroscopic gravitational source still represents an interesting open issue for further careful investigation.

Scattering of massless fermions by Schwarzschild and Reissner-Nordström black holes

“…Most of these studies have been dedicated to investigating different aspects of (massless) scalar wave scattering by black holes . However, there are also papers that studi the scattering of massless electromagnetic waves [24][25][26][27][28][29][30][31][32] and gravitational waves [33][34][35][36][37][38][39][40]. The problem of scattering of massive spinor 1/2 waves by black holes was discussed in [5,[41][42][43][44][45][46][47][48][49][50].The scattering of massless fermions was studied in [51,52], where the scattering of massless fermions by a black hole with a cosmic string, respectively a dilatonic black hole was investigated and partially in [46] for a Schwarzschild black hole.…”

GWsim: a code to simulate gravitational waves propagating in a potential well

“…If we consider the incident waves, the lensing system can be treated as a scattering system Weinberg (1972); Peters (1974); Takahashi et al (2005); Sorge (2015). Indeed, the scattering of waves by potential wells has been well studied in Quantum Mechanics.…”

Scattering from compact objects: Regge poles and the complex angular momentum method

“…A dimensionless parameter Mω ¼ πr g =λ encapsulates the ratio of the gravitational radius r g ¼ 2GM=c 2 to the wavelength λ; herein we adopt geometric units such that G ¼ c ¼ 1. The long-wavelength (Mω ≪ 1), short-wavelength (Mω ≫ 1) and intermediate regimes have been studied with a combination of perturbative [15,[20][21][22], semiclassical [10,23] and numerical methods. The s ¼ 0 (scalar) [2,7,12,13,24], s ¼ 1=2 (fermion) [14,18], s ¼ 1 (electromagnetic) [6,17,25] and s ¼ 2 (gravitational) cases [8,9,16] have all been addressed.…”