Revisit on ``Ruling out chaos in compact binary systems''
Revisit on ``Ruling out chaos in compact binary systems''
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DOI：
10.1103/physrevd.76.124004
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发表时间：
2007-12
影响因子：
5
通讯作者：
Xin Wu;Yi Xie
中科院分区：
文献类型：
--
作者：
Xin Wu;Yi Xie
完整的广义相对论要求混沌指标在不同的时空坐标系中对于一个给定的相对论动力学问题是不变的。在此基础上，采用带投影操作的双邻近轨道方法，以坐标时间为自变量，在不考虑引力辐射耗散效应的保守第二后牛顿（2PN）拉格朗日方程中计算了其中一个自旋致密双星的不变李雅普诺夫指数（LE）.在文献[J. D. Schnittman和F. A. Rasio，Phys. Rev. Lett. 87，121101（2001）]，而在另一个[N. J.康沃尔语和J.莱文，物理学评论快报。89，179001（2002）]并不主要依赖于重新缩放，而是由于LE的两种稍微不同的处理。对于前者，获得稳定极限值作为LE的可靠值比获得后者的拟合线的斜率（等于LE）花费更多的CPU时间。由于合并的一些黑洞，LE从前者不是一个自适应指标的混乱可比质量紧凑的双星。在这种情况下，两个邻近轨道的不变量更快的李雅普诺夫指标（FLI），作为一个非常敏感的工具，区分混沌和秩序，是值得推荐的。因此，我们再次发现在2PN近似通过随时间变化的不同比例的FLI的混沌。在真实的双星系统中确实不能排除混沌。«少
Full general relativity requires that chaos indicators should be invariant in various spacetime coordinate systems for a given relativistic dynamical problem. On the basis of this point, we calculate the invariant Lyapunov exponents (LEs) for one of the spinning compact binaries in the conservative second post-Newtonian (2PN) Lagrangian formulation without the dissipative effects of gravitational radiation, using the two-nearby-orbits method with projection operations and with coordinate time as an independent variable. It is found that the actual source leading to zero LEs in one paper [J. D. Schnittman and F. A. Rasio, Phys. Rev. Lett. 87, 121101 (2001)] but to positive LEs in the other [N. J. Cornish and J. Levin, Phys. Rev. Lett. 89, 179001 (2002)] does not mainly depend on rescaling, but is due to two slightly different treatments of the LEs. It takes much more CPU time to obtain the stabilizing limit values as reliable values of LEs for the former than to get the slopes (equal to LEs) of the fit lines for the latter. Due to coalescence of some of the black holes, the LEs from the former are not an adaptive indicator of chaos for comparable mass compact binaries. In this case, the invariantmore » fast Lyapunov indicator (FLI) of two-nearby orbits, as a very sensitive tool to distinguish chaos from order, is worth recommending. As a result, we do again find chaos in the 2PN approximation through different ratios of FLIs varying with time. Chaos cannot indeed be ruled out in real binaries.« less