标题： 四极-四极引力波 显示英文标题

标题： Quadrupole-quadrupole gravitational waves

摘要： 本文研究了由孤立系统产生的四极引力波的非线性自相互作用。 通过后闵可夫斯基算法，在系统的外部真空区域积分爱因斯坦场方程。 专注于四极-四极相互作用（二次非线性阶），我们得到了关于系统ADM质量和能量的非局部修正的已知结果，该修正考虑了四极波的辐射，并且得到了由于应力-能量分布重新辐射线性波而导致的非局部记忆效应。 然后我们计算了在四极-四极度规中与上述非局部效应相关的所有局部（瞬时）项。 在远离系统的远处展开度规，我们得到了相应的辐射场可观测量，包括所有非局部和瞬态贡献。 这尤其允许完成了可观测四极矩在5/2后牛顿阶的结果。 显示英文摘要

摘要： This paper investigates the non-linear self-interaction of quadrupole gravitational waves generated by an isolated system. The vacuum Einstein field equations are integrated in the region exterior to the system by means of a post-Minkowskian algorithm. Specializing in the quadrupole-quadrupole interaction (at the quadratic non-linear order), we recover the known results concerning the non-local modification of the ADM mass-energy of the system accounting for the emission of quadrupole waves, and the non-local memory effect due to the re-radiation by the stress-energy distribution of linear waves. Then we compute all the local (instantaneous) terms which are associated in the quadrupole-quadrupole metric with the latter non-local effects. Expanding the metric at large distances from the system, we obtain the corresponding radiation-field observables, including all non-local and transient contributions. This permits notably the completion of the observable quadrupole moment at the 5/2 post-Newtonian order.