Gravitational-wave tails of memory

TL;DR

This paper investigates higher-order tail effects in gravitational waves, specifically cubic tails-of-memory and spin-quadrupole tails, which influence the waveform at the 4PN order beyond quadrupolar radiation.

Contribution

It derives and analyzes the cubic tail effects, including tails-of-memory and spin-quadrupole tails, at the 4PN order in gravitational wave modeling.

Findings

Derived explicit expressions for tails-of-memory and spin-quadrupole tails.

Identified contributions of these tails to the gravitational waveform at 4PN order.

Enhanced understanding of non-linear gravitational wave effects.

Abstract

Gravitational-wave tails are linear waves that backscatter on the curvature of space-time generated by the total mass-energy of the source. The non-linear memory effect arises from gravitational waves sourced by the stress-energy distribution of linear waves themselves. These two effects are due to quadratic multipolar interactions (mass-quadrupole and quadrupole-quadrupole) and are well known. Also known are the tails generated by tails themselves (cubic "tails-of-tails") and the tails generated by tails-of-tails or vice versa (quartic "tails-of-tails-of-tails"). In this work, we focus on the cubic "tails-of-memory" corresponding to the mass-quadrupole-quadrupole interaction, as well as the "spin-quadrupole tails", which are due to the cubic interaction between the mass, the total angular momentum and the quadrupole. The tails-of-memory and the spin-quadrupole tails contribute to the asymptotic waveform at the fourth-post-Newtonian (4PN) order beyond quadrupolar radiation.