Universality of ultra-relativistic gravitational scattering

The eikonal approach to gravitational scattering and radiation at $$ \mathcal{O} $$(G3)

“…This contradiction became even sharper with ref. [15], where we first extended the analyticity-plus-crossing analysis of [32] to the ultrarelativistic massive case arriving at JHEP07(2021)169 exactly the same conclusions. However in ref.…”

“…On the contrary, it has become clear over the last few years that it consistently provides the necessary non-perturbative resummation to extract the proper classical limit of the amplitude and to calculate relevant classical observables in many different setups, including the scattering of objects with masses m 1 and m 2 , in the whole range m 1 +m 2 ≤ √ s < ∞, i.e. for generic relative velocities between the two bodies [12][13][14][15][16]. For these reasons, since the first direct detection of gravitational waves, the emphasis in the study of the eikonal exponentiation has naturally shifted towards its application to the classical relativistic two body problem, for which various GR techniques, like the PM expansion mentioned above, the post-Newtonian (PN) expansion, and the effective-one-body (EOB) approach [17] had been developed in the past to describe the inspiral phase of two merging black holes.…”

“…However in ref. [15] we also presented for the first time the solution of the puzzle. Following [13], but performing the calculation of the various loop diagrams taking into account the full soft region -rather its potential part -we computed the 2 → 2 scattering amplitude and the associated eikonal Re 2δ 2 in massive N = 8 supergravity at 3PM level and we found that the resulting deflection angle is free of log(s)-divergences, thus restoring agreement with [32] and the universality in the ultrarelativistic limit.…”

Quadratic-in-spin Hamiltonian at $$ \mathcal{O} $$(G2) from scattering amplitudes

“…[34] studied three-body dynamics, while refs. [35][36][37][38][39] incorporated the radiation emitted by the binary into their analysis. Refs.…”

Classical solutions and their double copy in split signature

“…Mathematically, the field strength operator essentially differentiates the exponential form of the coherent state once, pulling down the parameter of the state. The structure of this computation is strongly reminiscent of eikonal methods which have also been of interest as a method of connecting classical field theory to scattering amplitudes [32,37,40,48,54,55,[129][130][131][132][133][134][135][136][137][138][139][140][141][142][143][144][145].…”