Taming tree amplitudes in general relativity

We give a proof of BCFW recursion relations for all tree-level amplitudes ofgravitons in General Relativity. The proof follows the same basic steps as inthe BCFW construction and it is an extension of the one given for next-to-MHVamplitudes by one of the authors and P. Svr\v{c}ek in hep-th/0502160. The mainobstacle to overcome is to prove that deformed graviton amplitudes vanish asthe complex variable parameterizing the deformation is taken to infinity. Thisstep is done by first proving an auxiliary recursion relation where thevanishing at infinity follows directly from a Feynman diagram analysis. Theauxiliary recursion relation gives rise to a representation of gravityamplitudes where the vanishing under the BCFW deformation can be directlyproven. Since all our steps are based only on Feynman diagrams, our proofcompletely establishes the validity of BCFW recursion relations. This meansthat many results in the literature that were derived assuming their validitybecome true statements.Comment: 29 pages, v2: statement in the introduction corrected, appendix B added, reference added, JHEP styl