Tree Level Recursion Relations In General Relativity

TL;DR

This paper extends tree-level recursion relations from Yang-Mills theory to gravity, deriving new formulas for graviton scattering amplitudes and proving their validity for specific cases.

Contribution

It generalizes recursion relations to graviton amplitudes and provides explicit formulas for up to six gravitons, including the six graviton non-MHV case.

Findings

Derived new recursion relations for graviton amplitudes

Explicit formulas for all amplitudes up to six gravitons

Proved relations for MHV, next-to-MHV, and eight-graviton amplitudes

Abstract

Recently, tree-level recursion relations for scattering amplitudes of gluons in Yang-Mills theory have been derived. In this note we propose a generalization of the recursion relations to tree-level scattering amplitudes of gravitons. We use the relations to derive new simple formulae for all amplitudes up to six gravitons. In particular, we present an explicit formula for the six graviton non-MHV amplitude. We prove the relations for MHV and next-to-MHV n-graviton amplitudes and for all eight-graviton amplitudes.