Infrared features of gravitational scattering and radiation in the eikonal approach

Following a semiclassical eikonal approach—justified at transplanckian energies order by order in the deflection angle Θs∼4Gsb≡2Rb—we investigate the infrared features of gravitational scattering and radiation in four space-time dimensions, and we illustrate the factorization and cancellation of the infinite Coulomb phase for scattering and the eikonal resummation for radiation. As a consequence, both the eikonal phase 2δ(E,b) and the gravitational-wave (GW) spectrum dEGWdω are free from infrared problems in a frequency region extending from zero to (and possibly beyond) ω=1/R. The infrared-singular behavior of 4-D gravity leaves a memory in the deep infrared region (ωR≪ωb<1) of the spectrum. At O(ωb) we confirm the presence of logarithmic enhancements of the form already pointed out by Sen and collaborators on the basis of nonleading corrections to soft-graviton theorems. These, however, do not contribute to the unpolarized and/or azimuthally averaged flux. At O(ω2b2) we find instead a positive logarithmically enhanced correction to the total flux implying an unexpected maximum of its spectrum at ωb∼0.5. At higher orders we find subleading enhanced contributions as well, which can be resummed, and have the interpretation of a finite rescattering Coulomb phase of emitted gravitons.