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., 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 → NUB → SD. This gives an important indication for a transition in the black hole-black string system. © 2008 Elsevier B.V. All rights reserved.
Miyamoto, U., & Maeda, K. ichi. (2008). Liquid bridges and black strings in higher dimensions. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 664(1–2), 103–106. https://doi.org/10.1016/j.physletb.2008.05.010