Liquid bridges and black strings in higher dimensions

Abstract

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.

8 pages, 4 figures, 1 table; v2 reference added

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• Hagedorn Instability in Dimensionally Reduced Large-N Gauge Theories as Gregory-Laflamme and Rayleigh-Plateau Instabilities
• Black hole-black string phase transitions from hydrodynamics
• Curvature driven diffusion, Rayleigh-Plateau, and Gregory-Laflamme
• Critical Dimension and Negative Specific Heat in One-dimensional Large-N Reduced Models
• The Bernstein Conjecture, Minimal Cones, and Critical Dimensions
• One-Dimensional Approximation of Viscous Flows
• Complex Langevin Method on Rotating Matrix Quantum Mechanics at Thermal Equilibrium
• Stability of hypersurfaces with constant mean curvature trapped between two parallel hyperplanes
• D-dependence of gap between critical temperatures in one-dimensional gauge theories