arXiv 1301.61742013-01gr-qc

标量场和Yang-Mills场的双曲爱因斯坦物质演化和尾

Hyperboloidal Einstein-matter evolution and tails for scalar and Yang-Mills fields

Oliver Rinne, Vincent Moncrief

备注：: 28 pages, 9 figures. Minor changes to agree with journal version
DOI：: 10.1088/0264-9381/27/3/035014

摘要：

我们展示了如何可以包括在一个受约束的ADM的爱因斯坦方程的制定恒定的平均曲率表面。以前的结果的正则性方程在未来的零无穷远不受添加物质与tracefree能量动量张量。本文详细研究了共形耦合的标量场和杨-米尔斯场。我们首先在无对称性假设下导出方程，然后将其化为球对称。两个部门（重力和sphaleron）的球对称杨米尔斯场都包括在内。我们实现这个计划的数值，以研究晚时间的标量和杨米尔斯场耦合到爱因斯坦方程的尾巴。我们能够从规则的初始数据中演化出分散到平坦空间、吸积到给定的黑洞或坍缩到黑洞的时空。发现杨-米尔斯的sphaleron部门表现出一些非平凡的规范动力学。

英文摘要：

We show how matter can be included in a constrained ADM-like formulation of the Einstein equations on constant mean curvature surfaces. Previous results on the regularity of the equations at future null infinity are unaffected by the addition of matter with tracefree energy-momentum tensor. Two examples are studied in detail, a conformally coupled scalar field and a Yang-Mills field. We first derive the equations under no symmetry assumptions and then reduce them to spherical symmetry. Both sectors (gravitational and sphaleron) of the spherically symmetric Yang-Mills field are included. We implement this scheme numerically in order to study late-time tails of scalar and Yang-Mills fields coupled to the Einstein equations. We are able to evolve spacetimes that disperse to flat space, accrete onto a given black hole or collapse to a black hole from regular initial data. The sphaleron sector of Yang-Mills is found to exhibit some nontrivial gauge dynamics.

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英文摘要：

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