Continuing Isaacson's Legacy: A general metric theory perspective on gravitational memory and the non-linearity of gravity

TL;DR

This paper revisits Isaacson's approach to gravitational waves, demonstrating its connection to gravitational memory and providing a new method to compute displacement memory in various metric theories of gravity.

Contribution

It offers a general metric theory perspective on gravitational memory, extending Isaacson's work and linking it to the non-linearity of gravity.

Findings

Isaacson's approach implies displacement memory in gravity.

Provides an efficient method to compute gravitational memory.

Connects gravitational memory to the non-linearity of gravity.

Abstract

The challenge of defining a physical notion of gravitational waves, together with the associated dynamical degrees of freedom of a gravity theory, is a long-standing problem that famously lead to the discovery the Bondi-Metzner-Sachs (BMS) spacetime symmetry at null infinity and its connection to gravitational memory. Here, we show that the second major contribution to an understanding of waves in gravitation, attributed to the work of Isaacson, equally leads to the inevitable presence of displacement memory, and provides additional understanding of the phenomenon. In particular, the Isaacson viewpoint allows for an efficient method to compute gravitational displacement memory in general metric theories of gravity.