Gravitational self-force and the effective-one-body formalism between the innermost stable circular orbit and the light ring
Gravitational self-force and the effective-one-body formalism between the innermost stable circular orbit and the light ring
复制标题
DOI：
10.1103/physrevd.86.104041
复制
发表时间：
2012-09
影响因子：
5
通讯作者：
S. Akçay;L. Barack;T. Damour;N. Sago
中科院分区：
文献类型：
--
作者：
S. Akçay;L. Barack;T. Damour;N. Sago
我们计算保守片的引力自作用力（GSF）作用于一个粒子的质量M1，因为它移动沿着（不稳定）圆形测地轨道之间的最内层的稳定轨道和光环的史瓦西黑洞的质量M2？M1.更确切地说，我们构造函数huuR，L（x）？h？？R，Lu？u？（与德特韦勒的规范不变的“红移”变量），其中h？？R，L（？m1）是Lorenz规范中的正则化度量微扰，u？是m1在m2的背景史瓦西度规中的四速度，而x？【GC-3（m1+m2）？】2/3是从轨道频率？构造的不变坐标。特别地，我们探索了huuR，L在x=1/3的“光环”之外的行为（即，r= 3Gm 2/c2），其中圆形轨道变为零。利用最近发现的huuR，L和a（u）之间的联系，对称质量比？？m1 m2/（m1+m2）2，主径向势A（u，？）= 1-2u+？a（u）+O（？2)的有效单体（EOB）的形式主义，我们计算从我们的GSF数据EOB函数a（u）在整个区域0<u<1/3（从而扩展以前的结果限于u？1/5）。我们发现a（u）像a（u）一样发散？0.25（1-3u）-1/2在光环极限，u？（1/3）-，解释这种发散行为的物理起源，并讨论其后果的EOB形式主义。我们构造了a（u）的精确的全局解析拟合，在整个区域0<u<1/3（甚至更远）上都是有效的，并给出了a（u）及其前三阶导数在最内层稳定圆轨道u=1/6处的精确数值估计，以及相关的O（？）轨道频率的变化。在以前的工作中，我们使用GSF的数据，稍微偏心的轨道上计算一定的线性组合的a（u）和它的前两个衍生物，也涉及O（？）第二EOB径向电位D的一部分？(u)=1+？你是谁？(u)+O（？2）。结合这些结果与我们目前的全球解析表示（u），我们数值计算d？(u)在间隔0<u上？1/6
We compute the conservative piece of the gravitational self-force (GSF) acting on a particle of mass m1 as it moves along an (unstable) circular geodesic orbit between the innermost stable orbit and the light ring of a Schwarzschild black hole of mass m2?m1. More precisely, we construct the function huuR,L(x)?h??R,Lu?u? (related to Detweiler’s gauge-invariant “redshift” variable), where h??R,L(?m1) is the regularized metric perturbation in the Lorenz gauge, u? is the four-velocity of m1 in the background Schwarzschild metric of m2, and x?[Gc-3(m1+m2)?]2/3 is an invariant coordinate constructed from the orbital frequency ?. In particular, we explore the behavior of huuR,L just outside the “light ring” at x=1/3 (i.e., r=3Gm2/c2), where the circular orbit becomes null. Using the recently discovered link between huuR,L and the piece a(u), linear in the symmetric mass ratio ??m1m2/(m1+m2)2, of the main radial potential A(u,?)=1-2u+?a(u)+O(?2) of the effective-one-body (EOB) formalism, we compute from our GSF data the EOB function a(u) over the entire domain 0<u<1/3 (thereby extending previous results limited to u?1/5). We find that a(u) diverges like a(u)?0.25(1-3u)-1/2 at the light-ring limit, u?(1/3)-, explain the physical origin of this divergent behavior, and discuss its consequences for the EOB formalism. We construct accurate global analytic fits for a(u), valid on the entire domain 0<u<1/3 (and possibly beyond), and give accurate numerical estimates of the values of a(u) and its first three derivatives at the innermost stable circular orbit u=1/6, as well as the associated O(?) shift in the frequency of that orbit. In previous work we used GSF data on slightly eccentric orbits to compute a certain linear combination of a(u) and its first two derivatives, involving also the O(?) piece of a second EOB radial potential D? (u)=1+?d? (u)+O(?2). Combining these results with our present global analytic representation of a(u), we numerically compute d? (u) on the interval 0<u?1/6