任意拓扑中带电静电黑洞的存在性
On the existence of charged electrostatic black holes in arbitrary topology
AI总结：
本文研究任意拓扑下S1对称静态电真空黑洞的存在性，证明除Schwarzschild外，Boost与Myers-Korotkin-Nicolai真空黑洞无法带电并保持渐近行为，揭示3+1维中电荷、拓扑与渐近性的复杂关系。
摘要：
3+1维静态黑洞解的爱因斯坦方程的一般分类，无论有无物质，在广义相对论中处于核心地位，在几何学中也具有重要意义。在S1对称真空时空领域，最近的一项分类证明，在不限制拓扑或渐近行为的情况下，黑洞解只能有三种类型：(i) Schwarzschild黑洞，(ii) Boost黑洞，或(iii) Myers-Korotkin-Nicolai黑洞，每种类型都有其独特的渐近和拓扑类型。与此形成对比的是，关于S1对称静态电真空黑洞的一般分类所知甚少，尽管例子表明，从大的图景来看，与真空情形相比应该存在显著差异。那么一个基本问题是，是否存在与类型(i)、(ii)和(iii)的静态真空黑洞相对应的带电类似物。在本文中，我们证明了一个显著的事实：虽然可以对Schwarzschild解进行“充电”（得到Reissner-Nordström时空）并保持其渐近行为，但对Boost解和Myers-Korotkin-Nicolai解却不能这样做：添加小或大的电荷（如果可能的话）将完全改变它们的渐近行为。特别地，这类真空解不能被电磁扰动。本文的结果与Karlovini和Von Unge关于Reissner-Nordström黑洞的周期类似物的工作一致，但远远超出了这些工作。所得结果的类型以及所使用的技术基于Bakry-Émery风格的比较几何，并且在该背景下似乎是全新的。这些发现指出了在3+1维时空中渐近性、拓扑和电荷之间复杂的相互作用，这与高维中发生的情况显著不同。
英文摘要：
The general classification of 3+1-static black hole solutions of the Einstein equations, with or without matter, is central in General Relativity and important in geometry. In the realm of S1-symmetric vacuum spacetimes, a recent classification proved that, without restrictions on the topology or the asymptotic behavior, black hole solutions can be only of three kinds: (i) Schwarzschild black holes, (ii) Boost black holes, or (iii) Myers-Korotkin-Nicolai black holes, each one having its distinct asymptotic and topological type. In contrast to this, very little is known about the general classification of S1-symmetric static electrovacuum black holes although examples show that, on the large picture, there should be striking differences with respect to the vacuum case. A basic question then is whether or not there are charged analogs to the static vacuum black holes of types (i), (ii) and (iii). In this article we prove the remarkable fact that, while one can `charge' the Schwarzschild solution (resulting in a Reissner-Nordström spacetime) preserving the asymptotic, one cannot do the same to the Boosts and to the Myers-Korotkin-Nicolai solutions: the addition of a small or large electric charge, if possible at all, would transform entirely their asymptotic behavior. In particular, such vacuum solutions cannot be electromagnetically perturbed. The results of this paper are consistent but go far beyond the works of Karlovini and Von Unge on periodic analogs of the Reissner-Nordström black holes. The type of result as well as the techniques used are based on comparison geometry a la Bakry-Émery and appear to be entirely novel in this context. The findings point to a complex interplay between asymptotic, topology and charge in spacetime dimension 3+1, markedly different from what occurs in higher dimensions.
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