The dynamics of precessing binary black holes using the post-Newtonian approximation
The dynamics of precessing binary black holes using the post-Newtonian approximation
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DOI：
10.1103/physrevd.71.024027
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发表时间：
2004-07
影响因子：
5
通讯作者：
M. Hartl;A. Buonanno
中科院分区：
文献类型：
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作者：
M. Hartl;A. Buonanno
我们使用后牛顿（PN）运动方程的哈密顿公式研究了二元黑洞的（保守）动力学。我们使用的哈密顿量包括自旋-轨道耦合，自旋-自旋耦合，和质量自旋/自旋诱导四极相互作用项。我们调查的定性影响，这些条款的轨道;在准圆和偏心轨道的情况下，我们搜索的混沌的存在下（使用的方法的Lyapunov指数）为各种各样的初始条件。对于准圆轨道，我们发现总质量为10 - 40 M的黑洞在初始分离时没有混沌行为，对应于牛顿引力波（GW）频率小于150 Hz。只有对于相当小的初始径向距离（对应于大于150 Hz的GW频率），在径向分离中自旋-自旋诱导的振荡是相当重要的，我们才能找到混沌解，即使这样，它们也很罕见。此外，这些混沌准圆轨道的天体物理学意义值得怀疑，因为它们源自运动方程的直接参数化，而不是来自广泛分离的双星在引力辐射反应下演化为小分离。在高度偏心轨道的情况下，地面干涉仪是不是天体物理学的青睐，我们再次发现混乱的解决方案，但只有在近心如此之小，高阶PN校正，特别是更高的自旋PN校正，也应该考虑。两者合计，我们的调查准圆和偏心轨道发现混乱的轨道，要么是可疑的天体物理学的兴趣地面干涉仪或违反所需的近似运动方程是物理上有效的后牛顿秩序考虑。
We investigate the (conservative) dynamics of binary black holes using the Hamiltonian formulation of the post-Newtonian (PN) equations of motion. The Hamiltonian we use includes spin-orbit coupling, spinspin coupling, and mass monopole/spin-induced quadrupole interaction terms. We investigate the qualitative effects of these terms on the orbits; in the case of both quasicircular and eccentric orbits, we search for the presence of chaos (using the method of Lyapunov exponents) for a large variety of initial conditions. For quasicircular orbits, we find no chaotic behavior for black holes with total mass 10‐40M� when initially at a separation corresponding to a Newtonian gravitational-wave (GW) frequency less than � 150 Hz. Only for rather small initial radial distances (corresponding to a GW frequency larger than � 150 Hz), for which spin-spin induced oscillations in the radial separation are rather important, do we find chaotic solutions, and even then they are rare. Moreover, these chaotic quasicircular orbits are of questionable astrophysical significance, since they originate from direct parametrization of the equations of motion rather than from widely separated binaries evolving to small separations under gravitational radiation reaction. In the case of highly eccentric orbits, which for ground-based interferometers are not astrophysically favored, we again find chaotic solutions, but only at pericenters so small that higher order PN corrections, especially higher spin PN corrections, should also be taken into account. Taken together, our surveys of quasicircular and eccentric orbits find chaos only for orbits that are either of dubious astrophysical interest for ground-based interferometers or which violate the approximations required for the equations of motion to be physically valid at the post-Newtonian order considered.