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arXiv 1302.4161gr-qc
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Einstein-Rosen波的重整化群方法

Renormalization group approach to Einstein-Rosen waves

Tomohiro Harada, Sanjay Jhingan

摘要:

本文对具有全柱对称性的Einstein-Rosen波或真空时空进行了重整化群分析。我们发现自相似解在重整化群变换中表现为不动点。这些解分别对应于爆炸引力波和坍缩引力波的晚期和早期。基于对自相似解的线性微扰分析,我们得出结论:在没有入射波的情况下,自相似演化是爆炸引力波稳定的,而在坍缩引力波时是弱不稳定的.结果表明,自相似解可以描述爆炸引力波更一般解的渐近行为,从而将广义相对论中的相似性假设从球对称扩展到柱对称.

英文摘要:

We present a renormalization group analysis to Einstein-Rosen waves or vacuum spacetimes with whole-cylinder symmetry. It is found that self-similar solutions appear as fixed points in the renormalization group transformation. These solutions correspond to the explosive gravitational waves and the collapsing gravitational waves at late times and early times, respectively. Based on the linear perturbation analysis of the self-similar solutions, we conclude that the self-similar evolution is stable as explosive gravitational waves under the condition of no incoming waves, while it is weakly unstable as collapsing gravitational waves. The result implies that self-similar solutions can describe the asymptotic behavior of more general solutions for exploding gravitational waves and thus extends the similarity hypothesis in general relativity from spherical symmetry to cylindrical symmetry.

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