规则黑洞的一些整体、解析和拓扑性质
Some global, analytical and topological properties of regular black holes
摘要：
在这项工作中，我们从全局的角度来研究规则的黑洞寻找规避一些著名的奇异性定理，通过使用他们的“逆转”。然后，典型的球对称，（局部）静态的四维规则黑洞解的切片模型几何描述从分析和拓扑的角度来看。虽然围绕规则中心的切片的标量曲率和克雷奇曼曲率的有限性决定了核心的几何形状，但庞加莱猜想的肯定答案确保了，在两个假设下，它的拓扑结构是一个三球面。然而，通常，核被示出为$S^3$、$H^3$、$\mathbb{R}\times S^1$或$S^1\times S^2$，这取决于是否采用de Sitter、anti de Sitter、Nariai或Bertotti-Robinson几何形状来描述规则中心处的切片。然后，上述切片的塞弗特纤维空间的描述，以显示的欧拉特性的丛可以用来跟踪之间的过渡的核心的定期黑洞和其余的切片在大多数情况下考虑在文献中。在Geroch和Tipler定理被用来研究正则黑洞时空拓扑变化的后果之后，我们证明了Borde和Vilenkin的奇异性定理被用来限制它们可能的类型.最后，我们注意到Nariai核可以安全地用于构建规则的黑洞，而无需改变拓扑结构。
英文摘要：
In this work we study regular black holes from a global perspective looking for evading some of the well-known singularity theorems by using their "reverses". Then, model geometries for the slices of typical spherically symmetric, (locally) static four dimensional regular black hole solutions are described from both an analytical and a topological point of view. While the finiteness of both the scalar and Kretchmann curvature of the slices around the regular center determines the geometry of the core, the positive answer to the Poincaré conjecture assures that, under two assumptions, its topology is that of a three-sphere. However, in general, the cores are shown to be $S^3$, $H^3$, $\mathbb{R}\times S^1$ or $S^1\times S^2$, depending whether a de Sitter, anti de Sitter, Nariai or Bertotti-Robinson geometries are employed to describe the slices at the regular center. Then, a description of the aforementioned slices in terms of Seifert fibre spaces is given in order to show that the Euler characteristic of the bundle can be used to track the transition between the core of the regular black hole and the rest of the slices in most of the cases considered in the literature. After Geroch and Tipler's theorems are employed to study the consequences of topology change on regular black hole spacetimes, we show that Borde and Vilenkin's singularity theorem is used to restrict their possible types. We end by noting that Nariai cores can be safely used to construct regular black holes without topology changes.
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