On the classical limit of the (sub)$^{n}$-leading soft graviton theorems in $D = 4$ without deflection

TL;DR

This paper explores how infinite soft graviton theorems relate to classical gravitational scattering in four dimensions, revealing that the classical field at large impact parameters can be derived from these theorems, with specific frequency mode behaviors.

Contribution

It demonstrates that the infinite impact parameter limit of classical gravitational fields can be derived from soft graviton theorems beyond sub-leading order in four dimensions.

Findings

Classical gravitational fields at large impact parameters are linked to soft graviton theorems.

Modes scale as 5^{n}\u2212log5 with vanishing memory.

Soft theorems encode classical scattering information beyond sub-leading order.

Abstract

Tree-level gravitational amplitudes satisfy an infinite hierarchy of soft factorization theorems. The existence of these theorems has been recently linked with the existence of an infinite tower of asymptotic symmetries. In this paper, we analyze the relevance of the soft graviton theorems beyond sub-leading order in the context of classical gravitational scattering in four dimensions. More in detail, we show that the infinite impact parameter limit of the late-time gravitational field emitted during a classical scattering can be derived using these factorization theorems. The classical field obtained in this (infinite impact parameter) regime has an expansion in the frequency of the detector where the modes scale as $\omega^{n}\log{\omega}$ with a vanishing memory.