  We consider the eikonal phase associated with the gravitational scattering of
a highly energetic light particle off a very heavy object in AdS spacetime. A
simple expression for this phase follows from the WKB approximation to the
scattering amplitude and has been computed to all orders in the ratio of the
impact parameter to the Schwarzschild radius of the heavy particle. The eikonal
phase is related to the deflection angle by the usual stationary phase
relation. We consider the flat space limit and observe that for sufficiently
small impact parameters (or angular momenta) the eikonal phase develops a large
imaginary part; the inelastic cross-section is exactly the classical absorption
cross-section of the black hole. We also consider a double scaling limit where
the momentum becomes null simultaneously with the asymptotically AdS black hole
becoming very large. In the dual CFT this limit retains contributions from all
leading twist multi stress tensor operators, which are universal with respect
to the addition of higher derivative terms to the gravitational lagrangian. We
compute the eikonal phase and the associated Lyapunov exponent in the double
scaling limit.
