Nariai解的非一般性：I.渐近性与空间齐次扰动
Non-genericity of the Nariai solutions: I. Asymptotics and spatially homogeneous perturbations
摘要：
这是两篇论文中的第一篇，我们研究了广义Nariai解的渐近性及其与宇宙无毛猜想的关系。根据宇宙无毛猜想，正宇宙学常数的真空中爱因斯坦场方程的一般展开解是各向同性的，并且渐近地接近deSitter解.家庭的解决方案，我们介绍的“广义Nariai解决方案”，但是，显示出相当不寻常的渐近性，因此应该是非通用的在某种意义上。在本文中，我们列出了Nariai解的基本事实，并几何地刻画了它们的渐近行为。一个特别的结果是一个严格的证明，事实上，Nariai解决方案不具有光滑的共形边界。我们继续通过解释类空间均匀的解决方案的非通用性。结果表明，三类等距广义Nariai解的扰动与SchwarzschilddeSitter解的不同质量区有关.我们在这里工作的动机是准备第二篇论文专门研究的不稳定性的Nariai解决方案的Gowdy对称性。我们将特别感兴趣的新的和在原则上任意复杂的宇宙学黑洞解的建设。
英文摘要：
This is the first of two papers where we study the asymptotics of the generalized Nariai solutions and its relation to the cosmic no-hair conjecture. According to the cosmic no-hair conjecture, generic expanding solutions of Einstein's field equations in vacuum with a positive cosmological constant isotropize and approach the de-Sitter solution asymptotically. The family of solutions which we introduce as "generalized Nariai solutions", however, shows quite unusual asymptotics and hence should be non-generic in some sense. In this paper, we list basic facts for the Nariai solutions and characterize their asymptotic behavior geometrically. One particular result is a rigorous proof of the fact that the Nariai solutions do not possess smooth conformal boundaries. We proceed by explaining the non-genericity within the class of spatially homogeneous solutions. It turns out that perturbations of the three isometry classes of generalized Nariai solutions are related to different mass regimes of Schwarzschild de-Sitter solutions. A motivation for our work here is to prepare the second paper devoted to the study of the instability of the Nariai solutions for Gowdy symmetry. We will be particularly interested in the construction of new and in principle arbitrarily complicated cosmological black hole solutions.
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