  Investigations of high-energy graviton-graviton and gluon-gluon scattering
are performed in the leading eikonal approximation for the kinematic regime of
large center of mass energy and low momentum transfer. We find a double copy
relation between the amplitudes of the two theories to all loop orders when, on
the gauge theory side, we retain only the set of diagrams at each loop order
for which the collinear divergences cancel amongst themselves. For this to
happen the color structure of all diagrams in the set must be identical. Using
standard field theoretic methods, it is shown that this relation is reflected
in a similar double copy relationship between the classical shockwaves of the
two theories as well.
