Post-Newtonian Theory for Gravitational Waves
Post-Newtonian Theory for Gravitational Waves
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发表时间：
2013-10
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通讯作者：
L. Blanchet
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作者：
L. Blanchet
为了被目前的引力波探测器网络(LIGO、室女座、KAGRA)观测和分析，并预期未来的第三代地面探测器(爱因斯坦望远镜、宇宙探索者)和空间探测器(LISA)，激励紧凑双星--由中子星和/或黑洞在最终融合之前的演化后期组成的双星系统--需要从广义相对论中进行高精度的预测。这些非常相对论的系统的轨道动力学和发射的引力波可以用最先进的后牛顿理论精确地建模。在这篇文章中，我们回顾了多极后Minkowskian近似方案，它合并到标准的后牛顿展开，成为对一般孤立物质系统有效的单一形式。这种混合的近似方法(称为MPM-PN)已经成功地应用于紧致双星系统，得到了高达后四牛顿(4PN)水平的运动方程，以及超出爱因斯坦四极公式的4.5PN量级的引力波形和磁通。我们描述了在这种高的后牛顿计算中发挥作用的维度正则化，用于治愈紫外线和红外发散。详细介绍了几个里程碑式的结果：多极矩的定义，引力辐射反应，圆轨道的守恒动力学，紧致双星力学第一定律，以及引力波传播中的非线性效应(尾巴、迭代尾巴和非线性记忆)。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流和波形的影响。
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.