Abstract
Radiation reaction (RR) terms at the third post-Minkowskian (3PM) order have recently been found to be instrumental in restoring smooth continuity between the non-relativistic, relativistic, and ultra-relativistic (including the massless) regimes. Here we propose a new and intriguing connection between RR and soft (bremsstrahlung) theorems which short-circuits the more involved conventional loop computations. Although first noticed in the context of the maximally supersymmetric theory, unitarity and analyticity arguments support the general validity of this 3PM-order connection that we apply, in particular, to Einstein's gravity and to its Jordan-Brans-Dicke extension. In the former case we find full agreement with a recent result by Damour obtained through a very different reasoning.
Highlights
The gravitational scattering of classical objects at large impact parameter b is relevant for the study of the inspiral phase of black-hole binaries since it can be used to determine the parameters of the Effective-One-Body description
Gravitational scattering has been at the centre of renewed attention and has been recently investigated using a variety of techniques, including the use of quantum field theory (QFT) amplitudes to extract the relevant classical physics [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23]
We will focus in particular on the eikonal approach [24,25,26,27], where the classical gravitational dynamics is derived from standard QFT amplitudes by focusing on the terms that exponentiate in the eikonal phase e2iδ
Summary
The gravitational scattering of classical objects at large impact parameter b is relevant for the study of the inspiral phase of black-hole binaries since it can be used to determine the parameters of the Effective-One-Body description (see [1] and references therein). In this letter we expand on the approach discussed in [28,34] where the relation between the real and the imaginary part of δ2 was used to derive the 3PM scattering angle in the ultrarelativistic limit and to show that it is a universal feature of all gravitational theories in the two derivative approximation It was shown in [34] for N = 8 supergravity that taking into account the full soft region in the loop integrals was crucial to obtain a smooth interpolation between the behaviour of δ2 in the non-relativistic, i.e. PostNewtonian (PN), regime and the ultrarelativistic (or massless) one. The basic idea underlying all cases is that the calculation of Im 2δ2 from sewing tree-level, on shell, inelastic amplitudes is far simpler than the derivation of the full two-loop elastic amplitude even when focusing on just the classical contributions Both for GR and for N = 8, the infrared divergent piece of δ2 can be equivalently obtained exploiting the exponentiation of infrared divergences in momentum space for the elastic amplitude itself (details will be presented elsewhere).
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