On an Exponential Representation of the Gravitational S-Matrix

TL;DR

This paper introduces an exponential representation of the gravitational S-matrix that simplifies calculations and aligns with other methods in analyzing classical gravitational scattering, including radiation effects.

Contribution

It proposes a novel exponential S-matrix framework for gravitational scattering, differing from eikonal formalism, and demonstrates its effectiveness up to third Post-Minkowskian order.

Findings

Agreement with other approaches in gravitational scattering calculations

Inclusion of radiation reaction effects at third Post-Minkowskian order

Simplified computational rules for the S-matrix

Abstract

An exponential representation of the S-matrix provides a natural framework for understanding the semi-classical limit of scattering amplitudes. While sharing some similarities with the eikonal formalism it differs from it in details. Computationally, rules are simple because pieces that must be subtracted are given by combinations of unitarity cuts. Analyzing classical gravitational scattering to third Post-Minkowskian order in both maximal supergravity and Einstein gravity we find agreement with other approaches, including the contributions from radiation reaction terms. The kinematical relation for the two-body problem in isotropic coordinates follows immediately from this procedure, again with the inclusion of radiation reaction pieces up to third Post-Minkowskian order.