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arXiv 1601.07529gr-qc
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弯曲时空中扩展试验体的正则哈密顿量:自旋二次阶

Canonical Hamiltonian for an extended test body in curved spacetime: To quadratic order in spin

Justin Vines, Daniela Kunst, Jan Steinhoff, Tanja Hinderer

摘要:

我们推导出一个扩展的旋转测试机构在弯曲的背景时空,二次阶的自旋,在三维位置,动量和自旋变量具有规范泊松括号的哈密顿量。这需要仔细分析自旋补充条件的变化如何与身体的代表性世界线和身体的多极矩的变换有关,我们采用双张量演算来精确构建这种分析。我们将结果应用到克尔时空的情况下,从而计算一个明确的正则哈密顿量的测试体极限的自旋两体问题在广义相对论,有效的通用轨道和自旋取向,在测试自旋的二次顺序。这完全相对论性的哈密顿量,然后扩展后牛顿的订单和克尔自旋参数的权力,允许与现有的后牛顿结果的测试质量限制进行比较。完全相对论性哈密顿量及其展开的结果可以为构造波形模型,特别是有效单体模型提供信息,以分析来自致密双星的引力波。

英文摘要:

We derive a Hamiltonian for an extended spinning test body in a curved background spacetime, to quadratic order in the spin, in terms of three-dimensional position, momentum, and spin variables having canonical Poisson brackets. This requires a careful analysis of how changes of the spin supplementary condition are related to shifts of the body's representative worldline and transformations of the body's multipole moments, and we employ bitensor calculus for a precise framing of this analysis. We apply the result to the case of the Kerr spacetime and thereby compute an explicit canonical Hamiltonian for the test-body limit of the spinning two-body problem in general relativity, valid for generic orbits and spin orientations, to quadratic order in the test spin. This fully relativistic Hamiltonian is then expanded in post-Newtonian orders and in powers of the Kerr spin parameter, allowing comparisons with the test-mass limits of available post-Newtonian results. Both the fully relativistic Hamiltonian and the results of its expansion can inform the construction of waveform models, especially effective-one-body models, for the analysis of gravitational waves from compact binaries.

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