Tree Level Recursion Relations In General Relativity

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.

17 pp. v3: Fixed typos in six-graviton non-MHV amplitude, added references

References in corpus (12)

• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• New Recursion Relations for Tree Amplitudes of Gluons
• MHV Vertices And Tree Amplitudes In Gauge Theory
• Multi-Leg One-Loop Gravity Amplitudes from Gauge Theory
• On-Shell Recurrence Relations for One-Loop QCD Amplitudes
• All Next-to-Maximally-Helicity-Violating One-Loop Gluon Amplitudes in N=4 Super-Yang-Mills Theory
• Inherited Twistor-Space Structure of Gravity Loop Amplitudes
• Supersymmetry counterterms revisited
• Recursion Relations for Tree Amplitudes in Super Gauge Theories
• Dissolving N=4 loop amplitudes into QCD tree amplitudes
• Compact Formulas for Tree Amplitudes of Six Partons
• A Note on MHV Amplitudes for Gravitons

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