Log translation invariance of log soft gravitational radiation

TL;DR

This paper demonstrates how the universal logarithmic terms in soft gravitational radiation are invariant under log translations, revealing underlying symmetries and recurrence relations for higher-order terms.

Contribution

It introduces a framework that makes log translation invariance explicit in the soft gravitational radiation expansion, providing new insights into universal log soft terms.

Findings

Logarithmic translation invariance explains cancellation of certain contributions.

Recurrence relation for higher-order universal log soft terms.

Unified understanding of soft gravitational radiation's logarithmic structure.

Abstract

The gravitational radiation emitted during a classical scattering process is known to exhibit two universal logarithmic terms in its soft frequency expansion. We show that these terms can be written in a way that makes the action of \emph{logarithmic translations} manifest. Invariance under log translations naturally explains a puzzling cancellation in the contribution from outgoing massless particles and leads to a recurrence relation for expected higher-order universal log soft terms.