论文标题
紧凑型二进制二进制的四杆矩与纽顿之后的第四个秩序：关联谐波和辐射指标
The Quadrupole Moment of Compact Binaries to the Fourth post-Newtonian Order: Relating the Harmonic and Radiative Metrics
论文作者
论文摘要
通过紧凑型二元系统的第四次牛顿（4pn）引力波的完成，我们使用后夫斯基的扩展分析和对比了孤立系统之外的度量标准的不同结构。以前已经研究了“谐波”坐标中的度量标准，尤其是计算尾巴和记忆效应。但是，当$ r \ to \ infty $（带有$ t-r/c = $ const）时，径向距离$ r $的对数的力量困扰着它。结果，以4pn顺序进入引力波通量的“内存”效应的繁琐计算在所谓的“辐射”坐标中更有效地进行，该坐标承认，该坐标承认（邦德 - 类型）在无限的无限范围内的Infinity（bondi-type）扩展，无需任何对比$ r^{-1} $。在这里，我们考虑了一种特定的结构，并在后链球后的扩展中按顺序执行订单，该构造直接在辐射坐标中产生度量。我们将这两个结构联系起来，并证明它们在参数化辐射度量的“规范”矩之间的关系与谐波度量标准的“规范”矩之间是相等的。我们以4PN顺序为质量四极矩时量提供了适当的关系，这在推导对重力通量的“记忆尾部”贡献时至关重要。
Motivated by the completion of the fourth post-Newtonian (4PN) gravitational-wave generation from compact binary systems, we analyze and contrast different constructions of the metric outside an isolated system, using post-Minkowskian expansions. The metric in "harmonic" coordinates has been investigated previously, in particular to compute tails and memory effects. However, it is plagued by powers of the logarithm of the radial distance $r$ when $r\to\infty$ (with $t-r/c=$ const). As a result, the tedious computation of the "tail-of-memory" effect, which enters the gravitational-wave flux at 4PN order, is more efficiently performed in the so-called "radiative" coordinates, which admit a (Bondi-type) expansion at infinity in simple powers of $r^{-1}$, without any logarithms. Here we consider a particular construction, performed order by order in the post-Minkowskian expansion, which directly yields a metric in radiative coordinates. We relate both constructions, and prove that they are physically equivalent as soon as a relation between the "canonical" moments which parametrize the radiative metric, and those parametrizing the harmonic metric, is verified. We provide the appropriate relation for the mass quadrupole moment at 4PN order, which will be crucial when deriving the "tail-of-memory" contribution to the gravitational flux.
