Spacetime symmetries and linearization stability of the Einstein equations. I
Spacetime symmetries and linearization stability of the Einstein equations. I
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DOI：
10.1063/1.522814
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发表时间：
1975-03
影响因子：
1.3
通讯作者：
V. Moncrief
中科院分区：
文献类型：
--
作者：
V. Moncrief
在以前的论文中，我们开始研究的Fischer-Marsden条件的线性化稳定性的真空时空紧凑，柯西超曲面。我们证明了这类时空是线性化稳定的当且仅当它不存在全局Killing向量场。在本文中，我们推导出一般的非线性约束的扰动是必要的，只要Killing对称性发生，以排除虚假的扰动解。我们建立了超曲面的独立性，这些约束，将它们与保守积分的扰动方程与背景的Killing对称性。作为这个结果的推论，我们还建立了非线性约束的规范不变性。我们简要地讨论了非紧的情况下，并提到一个可能的应用程序，我们的结果的霍金过程的量子力学粒子生产的黑洞的研究。
In a previous paper we began a study of the Fischer–Marsden conditions for the linearization stability of vacuum space–times with compact, Cauchy hypersurfaces. We showed that a space–time of this class is linearization stable if and only if it admits no global Killing vector fields. In this paper we derive the general nonlinear constraints upon the perturbations which are necessary, whenever Killing symmetries occur, to exclude spurious perturbation solutions. We establish the hypersurface independence of these constraints by relating them to the conserved integrals of the perturbation equations associated with the Killing symmetries of the background. As a corollary of this result, we also establish the gauge invariance of the nonlinear constraints. We briefly discuss the noncompact case and mention a possible application of our results to the study of the Hawking process of quantum mechanical particle production by black holes.