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arXiv 1003.0239gr-qc
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玻色子双星的数值研究

A Numerical Study of Boson Star Binaries

Bruno C. Mundim

摘要:

本文描述了在广义相对论近似下对玻色子双星的数值研究。我们采用的近似对广义相对论的动力学变量(3度规的共形平坦性)和时空的时间切片(最大切片)施加了一定的限制。由此产生的建模问题需要一个耦合的非线性系统的4双曲型,5椭圆型偏微分方程(PDE)在三个空间维度和时间的解决方案。我们近似地解决这个系统作为一个初边值问题,使用有限差分技术和众所周知的,计算效率高的数值算法,如多重网格法的情况下的椭圆方程。仔细注意代码验证的问题,论文的一个关键部分是演示,有限差分离散化的基本规模减少,我们的数值代码产生的结果收敛到一个解决方案的连续系统的偏微分方程所需的。本文最后讨论了玻色子双星轨道动力学的一些初步探索的结果。特别是,我们描述的计算中,这样一个二进制的运动是遵循两个以上的轨道周期,这是一个显着的进步,比以前的研究。我们还提出了计算结果中的玻色子恒星合并,并有证据表明黑洞形成。

英文摘要:

This thesis describes a numerical study of binary boson stars within the context of an approximation to general relativity. The approximation we adopt places certain restrictions on the dynamical variables of general relativity (conformal flatness of the 3-metric), and on the time-slicing of the spacetime (maximal slicing). The resulting modeling problem requires the solution of a coupled nonlinear system of 4 hyperbolic, and 5 elliptic partial differential equations (PDEs) in three space dimensions and time. We approximately solve this system as an initial-boundary value problem, using finite difference techniques and well known, computationally efficient numerical algorithms such as the multigrid method in the case of the elliptic equations. Careful attention is paid to the issue of code validation, and a key part of the thesis is the demonstration that, as the basic scale of finite difference discretization is reduced, our numerical code generates results that converge to a solution of the continuum system of PDEs as desired. The thesis concludes with a discussion of results from some initial explorations of the orbital dynamics of boson star binaries. In particular, we describe calculations in which motion of such a binary is followed for more than two orbital periods, which is a significant advance over previous studies. We also present results from computations in which the boson stars merge, and where there is evidence for black hole formation.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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