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Classical subleading soft graviton theorem in four space-time dimensionsdetermines the gravitational wave-form at late and early retarded time,generated during a scattering or explosion, in terms of the four momenta of theingoing and outgoing objects. This result was `derived' earlier by taking theclassical limit of the quantum soft graviton theorem, and making someassumptions about how to deal with the infrared divergences of the soft factor.In this paper we give a direct proof of this result by analyzing the classicalequations of motion of gravity coupled to matter. We also extend the result tothe electromagnetic wave-form generated during scattering of charged particles,and present a new conjecture on subsubleading corrections to the gravitationalwave-form at early and late retarded time.

Proof of the Classical Soft Graviton Theorem in D=4