Double-logarithms in Einstein-Hilbert gravity and supergravity

We study the interplay between graviton reggeization and double-logarithmic in energy contributions to four-graviton scattering in theories with and without supersymmetry. Predictions to all orders in the gravitational coupling are given for these double-logarithms. As the number of supersymmetries grows these terms generate a convergent behaviour for the amplitudes at very high energies. At two-loop level, we find agreement with previous exact results for N=8 supergravity and with those of Boucher-Veronneau and Dixon, who studied the N=4,5,6 supergravities using a conjectured double-copy structure of gravity.