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arXiv 0905.1822gr-qchep-th
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静态数值相对论的新方法及其在Kaluza-Klein黑洞中的应用

A new approach to static numerical relativity, and its application to Kaluza-Klein black holes

Matthew Headrick, Sam Kitchen, Toby Wiseman

摘要:

我们提出了一个一般的框架,解决爱因斯坦方程的静态和欧几里得度量。首先,我们解决规范固定的问题,借用从Ricci流文献中所谓的DeTurck技巧,使爱因斯坦方程严格椭圆和推广通常的调和坐标规范。然后,我们研究了两种算法,Ricci流和牛顿的方法,解决所产生的Einstein-DeTurck方程。我们通过研究五维Kaluza-Klein理论中的局部黑洞和非均匀黑弦来说明这些方法的使用,改进了以前对其热力学和几何性质的计算。我们研究这些解决方案的各种运营商的频谱,特别是寻找负模式的Lichnerowicz运营商。我们将局部化的解决方案分为两个分支,满足在一个最低温度。我们找到了很好的证据,本地化和非均匀的解决方案之间的合并。我们还发现了一个狭窄的窗口的本地化的解决方案,具有负模式,但似乎有积极的比热。

英文摘要:

We propose a general framework for solving the Einstein equation for static and Euclidean metrics. First, we address the issue of gauge-fixing by borrowing from the Ricci-flow literature the so-called DeTurck trick, which renders the Einstein equation strictly elliptic and generalizes the usual harmonic-coordinate gauge. We then study two algorithms, Ricci-flow and Newton's method, for solving the resulting Einstein-DeTurck equation. We illustrate the use of these methods by studying localized black holes and non-uniform black strings in five-dimensional Kaluza-Klein theory, improving on previous calculations of their thermodynamic and geometric properties. We study spectra of various operators for these solutions, in particular finding negative modes of the Lichnerowicz operator. We classify the localized solutions into two branches that meet at a minimum temperature. We find good evidence for a merger between the localized and non-uniform solutions. We also find a narrow window of localized solutions that possess negative modes yet appear to have positive specific heat.

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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