Blanchet Luc
Institut d'Astrophysique de Paris, 98bis Boulevard Arago, 75014 Paris, France.
Living Rev Relativ. 2014;17(1):2. doi: 10.12942/lrr-2014-2. Epub 2014 Feb 13.
To be observed and analyzed by the network of gravitational wave detectors on ground (LIGO, VIRGO, etc.) and by the future detectors in space (LISA, etc.), inspiralling compact binaries - binary star systems composed of neutron stars and/or black holes in their late stage of evolution - require high-accuracy templates predicted by general relativity theory. The gravitational waves emitted by these very relativistic systems can be accurately modelled using a high-order post-Newtonian gravitational wave generation formalism. In this article, we present the current state of the art on post-Newtonian methods as applied to the dynamics and gravitational radiation of general matter sources (including the radiation reaction back onto the source) and inspiralling compact binaries. We describe the post-Newtonian equations of motion of compact binaries and the associated Lagrangian and Hamiltonian formalisms, paying attention to the self-field regularizations at work in the calculations. Several notions of innermost circular orbits are discussed. We estimate the accuracy of the post-Newtonian approximation and make a comparison with numerical computations of the gravitational self-force for compact binaries in the small mass ratio limit. The gravitational waveform and energy flux are obtained to high post-Newtonian order and the binary's orbital phase evolution is deduced from an energy balance argument. Some landmark results are given in the case of eccentric compact binaries - moving on quasi-elliptical orbits with non-negligible eccentricity. The spins of the two black holes play an important role in the definition of the gravitational wave templates. We investigate their imprint on the equations of motion and gravitational wave phasing up to high post-Newtonian order (restricting to spin-orbit effects which are linear in spins), and analyze the post-Newtonian spin precession equations as well as the induced precession of the orbital plane.
为了被地面引力波探测器网络（LIGO、VIRGO等）以及未来的空间探测器（LISA等）观测和分析，正在合并的致密双星——由处于演化后期的中子星和/或黑洞组成的双星系统——需要广义相对论理论预测的高精度模板。这些高度相对论性系统发出的引力波可以使用高阶后牛顿引力波产生形式精确建模。在本文中，我们介绍了后牛顿方法在一般物质源（包括源上的辐射反作用）的动力学和引力辐射以及正在合并的致密双星方面的当前技术水平。我们描述了致密双星的后牛顿运动方程以及相关的拉格朗日和哈密顿形式，注意计算中起作用的自场正则化。讨论了几个最内圆轨道的概念。我们估计后牛顿近似的精度，并与小质量比极限下致密双星引力自力的数值计算进行比较。得到了高阶后牛顿阶的引力波形和能量通量，并从能量平衡论证中推导出双星的轨道相位演化。对于偏心致密双星——在偏心率不可忽略的准椭圆轨道上运动的情况，给出了一些具有里程碑意义的结果。两个黑洞的自旋在引力波模板的定义中起着重要作用。我们研究它们对运动方程和引力波相位的影响，直至高阶后牛顿阶（限于自旋线性的自旋轨道效应），并分析后牛顿自旋进动方程以及轨道平面的诱导进动。
