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A study of the double logarithmic in the center-of-mass energy, $s$,contributions to the four-graviton scattering amplitude is presented forfour-dimensional ${\cal N} \geq 4$ supergravities. This includes a novelrepresentation for the coefficients of the perturbative expansion based onexactly solvable recurrences. A review is given of the structure in the complexangular momentum plane for the $t$-channel partial wave singularities of thedifferent amplitudes. Working in impact parameter representation, $\rho$, it isshown that the resummation of double logarithms makes gravity weaker in regionsof small $\rho$ and large $s$. This screening of the gravitational interactionat short distances in the double logarithmic sector of the amplitudes is moreacute as the number of gravitinos in the theory increases. It bringscorrections to the eikonal phase which can change the sign of the graviton'sdeflection angle and generate regions with repulsive interaction. For verysmall impact parameters there appears a constant negative shift in both theeikonal phase and Shapiro's time delay which is not large enough to generatecausality violation.

Double logarithms in ${\cal N} \geq 4$ supergravity: weak gravity and Shapiro's time delay