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arXiv 0912.3517gr-qcastro-ph.COastro-ph.GA
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自旋黑洞双星的改进的有效单体哈密顿量

An improved effective-one-body Hamiltonian for spinning black-hole binaries

Enrico Barausse, Alessandra Buonanno

摘要:

在最近的一篇论文中,我们计算了弯曲时空中自旋测试粒子的正则哈密顿量,在粒子自旋的线性阶上,我们计算了自旋黑洞双星的改进的有效单体(EOB)哈密顿量.与前面的描述一样,我们不仅赋予有效粒子质量m,而且赋予其自旋S*。因此,有效粒子与有效克尔背景(具有自旋S_Kerr)通过测地线型相互作用和与S* 成比例的附加自旋相关相互作用。当展开到后牛顿(PN)阶时,对于任意质量比,EOB哈密顿量再现了自旋-自旋耦合和自旋-轨道耦合到2.5PN阶。此外,它再现了测试粒子极限下的所有自旋轨道耦合。与试验粒子极限情况类似,当我们将EOB动力学限制为与轨道角动量对齐或反对齐的自旋时,EOB动力学具有几个有趣的特征,例如存在最内层稳定的圆形轨道,光子圆形轨道,以及在螺旋后的暴跌期间轨道频率的最大值。这些性质对于再现旋转黑洞双星的动力学和引力波发射至关重要,正如数值相对论模拟所计算的那样。

英文摘要:

Building on a recent paper in which we computed the canonical Hamiltonian of a spinning test particle in curved spacetime, at linear order in the particle's spin, we work out an improved effective-one-body (EOB) Hamiltonian for spinning black-hole binaries. As in previous descriptions, we endow the effective particle not only with a mass m, but also with a spin S*. Thus, the effective particle interacts with the effective Kerr background (having spin S_Kerr) through a geodesic-type interaction and an additional spin-dependent interaction proportional to S*. When expanded in post-Newtonian (PN) orders, the EOB Hamiltonian reproduces the leading order spin-spin coupling and the spin-orbit coupling through 2.5PN order, for any mass-ratio. Also, it reproduces all spin-orbit couplings in the test-particle limit. Similarly to the test-particle limit case, when we restrict the EOB dynamics to spins aligned or antialigned with the orbital angular momentum, for which circular orbits exist, the EOB dynamics has several interesting features, such as the existence of an innermost stable circular orbit, a photon circular orbit, and a maximum in the orbital frequency during the plunge subsequent to the inspiral. These properties are crucial for reproducing the dynamics and gravitational-wave emission of spinning black-hole binaries, as calculated in numerical relativity simulations.

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