更高维度中的液体桥和黑弦
Liquid bridges and black strings in higher dimensions
摘要：
分析高维扩展流体的毛细管极小化问题，我们发现黑洞-黑弦系统（Gregory-Laflamme不稳定性）和液滴-液桥系统（Rayleigh-Plateau不稳定性）之间存在惊人的相似性，这两个系统最初是用微扰方法提出的.在扩展的流体系统中，我们证实了临界尺寸的存在，在该临界尺寸以上，非均匀桥（NUB，即，{ \it Delaunay unduloid}）用作表面积的全局最小值。我们还发现了各种相结构（一个或两个尖点的体积面积相图）附近的临界尺寸。应用突变理论，我们预测，在9维（9D）空间和以下，我们有一个从均匀的桥（UB）到球形滴（SD）的一阶过渡，而在10维空间和以上，我们预计过渡，使UB $\to$ NUB $\to$ SD。这为黑洞-黑弦系统的跃迁提供了一个重要的指示。
英文摘要：
Analyzing a capillary minimizing problem for a higher-dimensional extended fluid, we find that there exist startling similarities between the black hole-black string system (the Gregory-Laflamme instability) and the liquid drop-liquid bridge system (the Rayleigh-Plateau instability), which were first suggested by a perturbative approach. In the extended fluid system, we confirm the existence of the critical dimension above which the non-uniform bridge (NUB, i.e., {\it Delaunay unduloid}) serves as the global minimizer of surface area. We also find a variety of phase structures (one or two cusps in the volume-area phase diagram) near the critical dimension. Applying a catastrophe theory, we predict that in the 9 dimensional (9D) space and below, we have the first order transition from a uniform bridge (UB) to a spherical drop (SD), while in the 10D space and above, we expect the transition such that UB $\to$ NUB $\to$ SD. This gives an important indication for a transition in the black hole-black string system.
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