Eikonal amplitudes from curved backgrounds

TL;DR

This paper develops a covariant method to compute eikonal scattering amplitudes in curved spacetimes, unifying long-distance gravitational interactions and revealing new factorization properties, including for Kerr black holes.

Contribution

It introduces a general covariant approach for calculating one-to-one eikonal amplitudes in curved backgrounds, extending previous results to Kerr spacetime and revealing novel factorization features.

Findings

Recovered known results for Schwarzschild scattering.

Derived a new exponentiation of amplitudes for Kerr black holes.

Identified a Kawai-Lewellen-Tye-like factorization in the amplitude.

Abstract

Eikonal exponentiation in QFT describes the emergence of classical physics at long distances in terms of a non-trivial resummation of infinitely many diagrams. Long ago, 't Hooft proposed a beautiful correspondence between ultra-relativistic scalar eikonal scattering and one-to-one scattering in a background shockwave space-time, bypassing the need to resum. In this spirit, we propose here a covariant method for computing one-to-one amplitudes in curved background space-times which gives rise what we conjecture to be a general expression for the eikonal amplitude. We show how the one-to-one scattering amplitude for scalars on any stationary space-time reduces to a boundary term that captures the long-distance behavior of the background and has the structure of an exponentiated eikonal amplitude. In the case of scalar scattering on Schwarzschild, we recover the known results for gravitational scattering of massive scalars in the eikonal regime. For Kerr, we find a remarkable exponentiation of the tree-level amplitude for gravitational scattering between a massive scalar and a massive particle of infinite spin. This amplitude exhibits a Kawai-Lewellen-Tye-like factorization, which we use to evaluate the eikonal amplitude in momentum space, and study its analytic properties.