A Classical Proof of the Classical Soft Graviton Theorem in D>4
Alok Laddha, Ashoke Sen
TL;DR
The paper addresses deriving the classical soft graviton theorem directly from classical gravity with matter in $D>4$. It uses a two-region spacetime decomposition and the flat-space retarded Green’s function to express low-frequency gravitational radiation in terms of asymptotic trajectories and spins, including radiation flux. The main result is a universal subleading soft-graviton formula, with explicit contributions from massless-field radiation encoded by $A^{\alpha}(\hat n')$ and $B^{\alpha\beta}(\hat n')$, and a demonstration that the radiative stress tensor reproduces the same soft factor. The work clarifies the classical-quantum correspondence of soft graviton emissions in higher dimensions and delineates the limitations at higher orders due to near-zone obstructions, while providing a foundation for extensions to higher-derivative theories.
Abstract
Classical soft graviton theorem gives an expression for the spectrum of low frequency gravitational radiation, emitted during a classical scattering process, in terms of the trajectories and spin angular momenta of ingoing and outgoing objects, including hard radiation. This has been proved to subleading order in the expansion in powers of frequency by taking the classical limit of the quantum soft graviton theorem. In this paper we give a direct proof of this result by analyzing the classical equations of motion of a generic theory of gravity coupled to interacting matter in space-time dimensions larger than four.