The Eikonal Approach to Gravitational Scattering and Radiation at $\mathcal{O}(G^3)$

Abstract

Using $\mathcal{N}=8$ 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 $\mathcal{N}=8$ 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.

88 pages, 7 figures, 2 ancillary files. v2: minor revisions, to appear in JHEP

References in corpus (9)

• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Algorithm FIRE -- Feynman Integral REduction
• Sixth post-Newtonian local-in-time dynamics of binary systems
• Gravitational Bremsstrahlung in the Post-Minkowskian Effective Field Theory
• Eikonal phase matrix, deflection angle and time delay in effective field theories of gravity
• From amplitudes to gravitational radiation with cubic interactions and tidal effects
• Towards an S-matrix Description of Gravitational Collapse
• Infrared features of gravitational scattering and radiation in the eikonal approach
• Rescattering corrections and self-consistent metric in Planckian scattering

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