To be observed and analyzed by the network of current gravitational-wave detectors (LIGO, Virgo, KAGRA), and in anticipation of future third generation ground-based (Einstein Telescope, Cosmic Explorer) and space-borne (LISA) detectors, inspiralling compact binaries—binary star systems composed of neutron stars and/or black holes in their late stage of evolution prior the final coalescence—require high-accuracy predictions from general relativity. The orbital dynamics and emitted gravitational waves of these very relativistic systems can be accurately modelled using state-of-the-art post-Newtonian theory. In this article we review the multipolar-post-Minkowskian approximation scheme, merged to the standard post-Newtonian expansion into a single formalism valid for general isolated matter system. This cocktail of approximation methods (called MPM-PN) has been successfully applied to compact binary systems, producing equations of motion up to the fourth-post-Newtonian (4PN) level, and gravitational waveform and flux to 4.5PN order beyond the Einstein quadrupole formula. We describe the dimensional regularization at work in such high post-Newtonian calculations, for curing both ultra-violet and infra-red divergences. Several landmark results are detailed: the definition of multipole moments, the gravitational radiation reaction, the conservative dynamics of circular orbits, the first law of compact binary mechanics, and the non-linear effects in the gravitational-wave propagation (tails, iterated tails and non-linear memory). We also discuss the case of compact binaries moving on eccentric orbits, and the effects of spins (both spin-orbit and spin–spin) on the equations of motion and gravitational-wave energy flux and waveform.

通过当前引力波探测器网络（LIGO、Virgo、KAGRA）进行观测和分析，并展望未来第三代地基（爱因斯坦望远镜、宇宙探索者）和星载（LISA）探测器，激发紧凑型双星——由中子星和/或黑洞组成的双星系统，处于最终合并之前的演化后期——需要广义相对论的高精度预测。这些相对论性系统的轨道动力学和发射的引力波可以使用最先进的后牛顿理论进行精确建模。在本文中，我们回顾了多极后闵可夫斯基近似方案，该方案与标准后牛顿展开式合并为对一般孤立物质系统有效的单一形式主义。这种近似方法的混合物（称为 MPM-PN）已成功应用于紧凑的二元系统，产生高达第四后牛顿 (4PN) 级的运动方程，以及超越爱因斯坦四极杆的 4.5PN 级的引力波形和通量公式。我们描述了在如此高的后牛顿计算中起作用的尺寸正则化，用于解决紫外线和红外线发散。详细介绍了几个具有里程碑意义的结果：多极矩的定义、引力辐射反应、圆形轨道的保守动力学、紧致二元力学第一定律以及引力波传播中的非线性效应（尾部、迭代尾部和非线性存储器）。我们还讨论了致密双星在偏心轨道上运动的情况，以及自旋（自旋轨道和自旋-自旋）对运动方程和引力波能量通量和波形的影响。