三阶自旋耦合的双黑洞系统混沌研究

发布时间：2018-04-20 20:27

本文选题：自旋致密双星 + 混沌　；参考：《南昌大学》2014年硕士论文

【摘要】：对于未来的引力波探测而言，，致密双星系统是最有前途的引力波波源。它由中子星或黑洞组成，是一个高度非线性和不可积的相对论二体问题，蕴含着丰富的共振和混沌现象。近年来，随着人们对引力波的探测越来越感兴趣，对致密双星系统的研究也成为了一个热点。本文的主要内容就是研究三阶自旋致密双星系统的混沌现象。我们考虑的是两个自旋黑洞的完整的三阶后牛顿（3PN）保守哈密顿方程，其中轨道部分精确到了3PN阶，自旋-轨道部分精确到了2.5PN阶，自旋-自旋部分精确到了3PN阶。它是一个十二维的系统，包含了总能量、三个总角动量共四个独立的首次积分，所以它是一个不可积系统。一方面通过数值积分我们发现3PN自旋-自旋耦合项在混沌现象中发挥着重要作用，它使系统更容易发生混沌现象。这是因为混沌现象的发生完全是由于自旋-自旋耦合项作用引起的，尤其是3PN自旋-自旋耦合项的贡献导致了系统的非线性强度急剧的增强。另一方面，通过对三阶自旋致密双星系统的参数扫描找到了很多混沌轨道，其中很多轨道的初始半径是大于10M的，并且它们的李雅普诺夫时间是小于双星并和时间的，也就是说它们在并和前就混沌了。
[Abstract]:For the future gravitational wave detection, the dense binary system is the most promising gravitational wave source. It consists of neutron stars or black holes. It is a highly nonlinear and non-integrable relativistic two-body problem with abundant resonance and chaos phenomena. In recent years, with the increasing interest in gravitational wave detection, the study of dense binary system has become a hot spot. The main content of this paper is to study the chaotic phenomena of the third order spin dense binary system. We consider the complete third-order post-Newtonian 3PN) conservative Hamiltonian equation of two spin black holes, in which the orbital part is accurate to 3PN order, the spin orbit part to 2.5PN order, and the spin spin part to 3PN order. It is a twelve dimensional system that contains the total energy, three total angular momentum, four independent first integrals, so it is a non-integrable system. On the one hand, we find that the 3PN spin-spin coupling term plays an important role in chaotic phenomena by numerical integration, which makes the system more prone to chaotic phenomena. This is due to the fact that the occurrence of chaos is entirely due to the spin-spin coupling term, especially the contribution of the 3PN spin-spin coupling term, which leads to a sharp increase in the nonlinear strength of the system. On the other hand, by scanning the parameters of the third order spin compact binary system, many chaotic orbits are found, many of which have an initial radius greater than 10m, and their Lyapunov time is smaller than that of binary stars and time. In other words, they are chaotic before and before.
【学位授予单位】：南昌大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：P145.8

【共引文献】