Gravitational-wave tails of memory
David Trestini, Luc Blanchet
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 nonlinear 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 order beyond quadrupolar radiation.