Notes on AdS-Schwarzschild eikonal phase

TL;DR

This paper analyzes the eikonal phase in AdS-Schwarzschild spacetime, deriving a simple all-orders expression, exploring its flat space limit, and connecting it to black hole absorption and dual CFT behavior.

Contribution

It provides a new all-orders expression for the eikonal phase in AdS, explores its inelastic and absorption properties, and studies the double scaling limit relevant for dual CFTs.

Findings

Eikonal phase derived to all orders in impact parameter ratio.

Large imaginary part of phase indicates black hole absorption.

Universal contributions from leading twist multi stress tensor operators.

Abstract

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.