Gravitational Memory, BMS Supertranslations and Soft Theorems

TL;DR

This paper demonstrates that gravitational radiation causes a measurable displacement memory effect, which is mathematically equivalent to Weinberg's soft graviton theorem, linking observable memory to fundamental quantum properties of gravity.

Contribution

It provides an explicit expression for BMS supertranslations caused by gravitational radiation and connects the memory effect to soft graviton theorems.

Findings

Displacement memory effect is linked to BMS supertranslations.

Explicit formula relates radiation flux moments to supertranslations.

Memory effect matches Weinberg's soft graviton production formula.

Abstract

The transit of a gravitating radiation pulse past arrays of detectors stationed near future null infinity in the vacuum is considered. It is shown that the relative positions and clock times of the detectors before and after the radiation transit differ by a BMS supertranslation. An explicit expression for the supertranslation in terms of moments of the radiation energy flux is given. The relative spatial displacement found for a pair of nearby detectors reproduces the well-known and potentially measurable gravitational memory effect. The displacement memory formula is shown to be equivalent to Weinberg's formula for soft graviton production.