Subleading non linear gravitational memory effect

TL;DR

This paper introduces a novel method using null geodesics to detect and analyze the subleading non-linear gravitational memory effect, connecting conserved charges with boundary shifts in a compactified spacetime.

Contribution

It develops a new approach to identify subleading gravitational memory effects through conserved charges in Newman-Unti gauge, extending understanding of non-linear gravitational phenomena.

Findings

Bulk memory detected in Newman-Unti gauge.

Conserved charges relate to gravitational memory at subleading orders.

Displacement in the radial direction corresponds to relative radius change.

Abstract

We apply the new method based on null geodesics for detecting gravitational memory and find the bulk memory in Newman-Unti gauge around the boundary of the conformally compactified space time. We show how we use the newly found conserved charges in the subleading orders of large-$r$ expansion of the BMS charges to define the gravitational memory at each order in the non-linearised gravitational theory. We also find the gravitational shift in the $r$ direction. It is shown that the longitudinal displacement at order $1/r$ is the relative radius change between two detectors derived by Strominger and Zhiboedov.