Notes on AdS-Schwarzschild eikonal phase

Understand

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.