Effective one body approach to the dynamics of two spinning black holes with next-to-leading order spin-orbit coupling
Effective one body approach to the dynamics of two spinning black holes with next-to-leading order spin-orbit coupling
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DOI：
10.1103/physrevd.78.024009
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发表时间：
2008-03
影响因子：
5
通讯作者：
T. Damour;P. Jaranowski;G. Schāfer
中科院分区：
文献类型：
--
作者：
T. Damour;P. Jaranowski;G. Schāfer
利用一个新的自旋双星引力相互作用的哈密顿公式，我们将两个自旋黑洞动力学的有效单体(EOB)描述扩展到自旋-轨道相互作用的次优有序(NLO)。依赖于自旋的EOB哈密顿量由四个主要部分构成：(I)有效哈密顿量和‘实’哈密顿量之间的变换；(Ii)包含动量高次方的广义有效哈密顿-雅可比方程；(Iii)Kerr型有效度规(具有Pade恢复系数)，它依赖于一些基本的‘有效自旋矢量’S{subef}的选择，并由可比质量效应变形；以及(Iv)一个额外的包含另一个自旋矢量{sigma}的有效自旋-轨道相互作用项。作为新的NLO自旋相关EOB哈密顿量的首次应用，我们计算了圆轨道(对于平行自旋)的结合能作为轨道频率和自旋参数的函数。我们还研究了最后一个稳定的圆轨道的特征：结合能、轨道频率和相应的无量纲自旋参数a{subLSO}{等同_to}Cj{subLSO}/(G(H{subLSO}/c{sup2}){sup2})。我们发现，NLO自旋轨道项的加入对大自旋和平行自旋的圆形轨道的动力学特性有显著的“缓和”作用。
Using a recent, novel Hamiltonian formulation of the gravitational interaction of spinning binaries, we extend the effective one body (EOB) description of the dynamics of two spinning black holes to next-to-leading order (NLO) in the spin-orbit interaction. The spin-dependent EOB Hamiltonian is constructed from four main ingredients: (i) a transformation between the 'effective' Hamiltonian and the 'real' one; (ii) a generalized effective Hamilton-Jacobi equation involving higher powers of the momenta; (iii) a Kerr-type effective metric (with Pade-resummed coefficients) which depends on the choice of some basic 'effective spin vector' S{sub eff}, and which is deformed by comparable-mass effects; and (iv) an additional effective spin-orbit interaction term involving another spin vector {sigma}. As a first application of the new, NLO spin-dependent EOB Hamiltonian, we compute the binding energy of circular orbits (for parallel spins) as a function of the orbital frequency, and of the spin parameters. We also study the characteristics of the last stable circular orbit: binding energy, orbital frequency, and the corresponding dimensionless spin parameter a{sub LSO}{identical_to}cJ{sub LSO}/(G(H{sub LSO}/c{sup 2}){sup 2}). We find that the inclusion of NLO spin-orbit terms has a significant 'moderating' effect on the dynamical characteristics of the circular orbits for large and parallel spins.