Recursion Relations for one-loop gravity amplitudes

We study the application of recursion relations to the calculation of finiteone-loop gravity amplitudes. It is shown explicitly that the known four, five,and six graviton one-loop amplitudes for which the external legs have identicaloutgoing helicities, and the four graviton amplitude with helicities (-,+,+,+)can be derived from simple recursion relations. The latter amplitude is derivedby introducing a one-loop three-point vertex of gravitons of positive helicity,which is the counterpart in gravity of the one-loop three-plus vertex inYang-Mills. We show that new issues arise for the five point amplitude withhelicities (-,+,+,+,+), where the application of known methods does not appearto work, and we discuss possible resolutions.Comment: 28 pages, LaTeX, 12 figures. v2:typos and references correcte