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

Abstract

Using $$ \mathcal{N} $$ N = 8 supergravity as a theoretical laboratory, we extract the 3PM gravitational eikonal for two colliding massive scalars from the classical limit of the corresponding elastic two-loop amplitude. We employ the eikonal phase to obtain the physical deflection angle and to show how its non-relativistic (NR) and ultra-relativistic (UR) regimes are smoothly connected. Such a smooth interpolation rests on keeping contributions to the loop integrals originating from the full soft region, rather than restricting it to its potential sub-region. This task is efficiently carried out by using the method of differential equations with complete near-static boundary conditions. In contrast to the potential-region result, the physical deflection angle includes radiation-reaction contributions that are essential for recovering the finite and universal UR limit implied by general analyticity and crossing arguments. We finally discuss the real emission of massless states, which accounts for the imaginary part of the 3PM eikonal and for the dissipation of energy-momentum. Adopting a direct approach based on unitarity and on the classical limit of the inelastic tree-level amplitude, we are able to treat $$ \mathcal{N} $$ N = 8 and General Relativity on the same footing, and to complete the conservative 3PM eikonal in Einstein’s gravity by the addition of the radiation-reaction contribution. We also show how this approach can be used to compute waveforms, as well as the differential and integrated spectra, for the different radiated massless fields.

Radiative classical gravitational observables at $$ \mathcal{O} $$(G3) from scattering amplitudes

“…[23,24] verified the low-velocity limit up to O(v 4 ) and O(v 7 ) respectively, from a world-line EFT perspective, and ref. [105] reproduced our result with full velocity dependence using methods similar to ref. [85].…”

“…In section 7 we present the final results for the gravitational impulse in N = 8 supergravity and general relativity and we investigate universality in the high-energy limit and the relation to the eikonal calculation in refs. [103,105]. We close with our conclusions and an outlook to future directions.…”

“…In the course of this work, we learned from an independent computation of several of the two-loop soft master integrals by Di Vecchia, Heissenberg, Russo, and Veneziano [105] in the context of the eikonal approach to classical gravitational scattering. We are grateful for discussions and comparisons as well as for coordinating publication.…”

“…Lastly, our virtual master integrals have been checked against an independent calculation [105]. Each integral has been checked to the maximum order of that has been computed in both papers.…”

Classical observables from coherent-spin amplitudes

“…In particular, many state-of-the-art post-Minkowskian (PM) computations of the two-body dynamics of Schwarzschild and Kerr black holes have been performed using the philosophy of effective field theory (EFT), either in the genuinely quantum-theoretic sense [3][4][5][6][7][8] or in the form of classical worldline effective theory [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24], see also refs. [25][26][27][28][29][30][31][32] for concurrent developments using eikonal methods.…”