  The eikonal phase which determines the Regge limit of the gravitational
scattering amplitude of a light particle off a heavy one in Minkowski
spacetimes admits an expansion in the ratio of the Schwarzschild radius of the
heavy particle to the impact parameter. Such an eikonal phase in AdS spacetimes
of any dimensionality has been computed to all orders and reduces to the
corresponding Minkowski result when both the impact parameter and the
Schwarzschild radius are much smaller than the AdS radius. The leading term in
the AdS eikonal phase can be reproduced in the dual CFT by a single stress
tensor conformal block, but the subleading term is a result of an infinite sum
of the double stress tensor contributions. We provide a closed form expression
for the OPE coefficients of the leading twist double stress tensors in four
spacetime dimensions and perform the sum to compute the corresponding lightcone
behavior of a heavy-heavy-light-light CFT correlator. The resulting compact
expression passes a few nontrivial independent checks. In particular, it agrees
with the subleading eikonal phase at large impact parameter.
