# Leading Singularities and Classical Gravitational Scattering

## TL;DR

This paper introduces a novel method using leading singularities to extract classical gravitational scattering amplitudes of two massive particles, providing compact formulas and connecting to post-Newtonian results.

## Contribution

It demonstrates how leading singularities can be used to obtain classical gravitational scattering amplitudes, including one-loop and higher-loop results, with new compact formulas.

## Key findings

- Leading singularities contain all classical information at one-loop.
- Derived a compact formula for relativistic classical one-loop scattering.
- Non-relativistic limit matches known post-Newtonian results.

## Abstract

In this work we propose to use leading singularities to obtain the classical pieces of amplitudes of two massive particles whose only interaction is gravitational. Leading singularities are generalizations of unitarity cuts. At one-loop we find that leading singularities obtained by multiple discontinuities in the t-channel contain all the classical information. As the main example, we show how to obtain a compact formula for the fully relativistic classical one-loop contribution to the scattering of two particles with different masses. The non-relativistic limit of the leading singularity agrees with known results in the post-Newtonian expansion. We also compute a variety of higher loop leading singularities including some all-loop families and study some of their properties.