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 Theta(s) similar to 4G root s/b equivalent to 2R/b - 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 2 delta(E, b) and the gravitational-wave (GW) spectrum dE(GW)/d omega are free from infrared problems in a frequency region extending from zero to (and possibly beyond) omega = 1/R. The infrared-singular behavior of 4-D gravity leaves a memory in the deep infrared region (omega R << omega b < 1) of the spectrum. At O(omega b) 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(omega(2)b(2)) we find instead a positive logarithmically enhanced correction to the total flux implying an unexpected maximum of its spectrum at omega b similar to 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.