Proof of the Classical Soft Graviton Theorem in D=4

TL;DR

This paper provides a direct classical proof of the subleading soft graviton theorem in four dimensions, extending it to electromagnetic waves and proposing a new conjecture on higher-order corrections.

Contribution

It offers a direct classical derivation of the soft graviton theorem and extends the result to electromagnetic waves, also proposing a new conjecture on subsubleading corrections.

Findings

Classical equations of motion confirm the soft graviton theorem without quantum assumptions.

Extension of the theorem to electromagnetic wave-forms during scattering.

Proposal of a new conjecture on subsubleading gravitational wave corrections.

Abstract

Classical subleading soft graviton theorem in four space-time dimensions determines the gravitational wave-form at late and early retarded time, generated during a scattering or explosion, in terms of the four momenta of the ingoing and outgoing objects. This result was `derived' earlier by taking the classical limit of the quantum soft graviton theorem, and making some assumptions 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 classical equations of motion of gravity coupled to matter. We also extend the result to the electromagnetic wave-form generated during scattering of charged particles, and present a new conjecture on subsubleading corrections to the gravitational wave-form at early and late retarded time.