On-Shell Recursion Relations in General Relativity
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This thesis is a study of the validity and application of the on-shell recursion relations within the theory of General Relativity. These relations are also known as the Britto-Cachazo-Feng-Witten (BCFW) relations. They reduce the calculation of a tree-level graviton scattering amplitude into the evaluation of two smaller physical amplitudes and of a propagator. With multiple applications of the recursion relations, amplitudes can be uniquely constructed from fundamental three-graviton amplitudes. The BCFW prescriptions were first applied to gauge theory. We thus provide a self-contained description of their usage in this context. We then generalize the proof of their validity to include gravity. The BCFW recursion relations can then be used to reconstruct the full theory from cubic vertices. We finally describe how these three-graviton vertices can be determined uniquely from Poincare symmetries.