The sky pattern of the linearized gravitational memory effect

TL;DR

This paper analyzes the linearized gravitational memory effect, showing that known sources produce E-mode patterns and that B-mode memory is likely primordial, with no other sources possible under reasonable conditions.

Contribution

It demonstrates that only known sources produce E-mode memory and that B-mode memory originates from primordial waves, ruling out other sources in linearized theory.

Findings

Known sources produce E-mode patterns in gravitational memory.

B-mode memory is of primordial origin, not from known sources.

No other physically reasonable sources can produce additional memory patterns.

Abstract

The gravitational memory effect leads to a net displacement in the relative positions of test particles. This memory is related to the change in the strain of the gravitational radiation field between infinite past and infinite future retarded times. There are three known sources of the memory effect: (i) the loss of energy to future null infinity by massless fields or particles, (ii) the ejection of massive particles to infinity from a bound system and (iii) homogeneous, source-free gravitational waves. In the context of linearized theory, we show that asymptotic conditions controlling these known sources of the gravitational memory effect rule out any other possible sources with physically reasonable stress-energy tensors. Except for the source-free gravitational waves, the two other known sources produce gravitational memory with E-mode radiation strain, characterized by a certain curl-free sky pattern of their polarization. Thus our results show that the only known source of B-mode gravitational memory is of primordial origin, corresponding in the linearized theory to a homogeneous wave entering from past null infinity.