Hereditary effects in gravitational radiation

This paper derives the leading nonlinear hereditary effects in the generation of gravitational radiation, i.e., the terms in the wave form which depend in an irreducible manner on the entire past history of the source. At the quadratically nonlinear order there are two types of hereditary contributions. The first ones are due to the readiation of gravitational waves by the stress-energy distribution of (linear) gravitational waves, and give rise to a net cumulative change in the wave form of bursts ("memory effect"). The second ones come from the backscattering of (linear) gravitational waves emitted in the past onto the constant curvature associated with the total mass of the source ("gravitational-wave tails"). An extension of a previously proposed multipole-moment wave generation formalism allows us to compute explicitly the wave form, including hereditary contributions, up to terms of fractional order ${\left(\frac{v}{c}\right)}^4$. Our results are derived for slow-moving systems of bodies, independently of the strength of their internal gravity. The tail contribution to the far wave-zone field is found to be fully consistent with a corresponding hereditary contribution to the gravitational radiation damping previously derived from a study of the near-zone field.