TY - JOUR

T1 - Liquid bridges and black strings in higher dimensions

AU - Miyamoto, Umpei

AU - Maeda, Kei ichi

N1 - Funding Information:
We would like to thank O.J.C. Dias for suggesting a possible extension of his work, and B. Kol and R. Emparan for fruitful discussions. U.M. is supported by the Golda Meir Fellowship, by The Israel Science Foundation grant No. 607/05, and by the DIP grant H.52. This work is partially supported by the Grant-in-Aid for Scientific Research Fund of the JSPS (No. 19540308) and for the Japan–UK Research Cooperative Program, and by the Waseda University Grants for Special Research Projects and for the 21st-Century COE Program at Waseda University.

PY - 2008/6/12

Y1 - 2008/6/12

N2 - 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.

AB - 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.

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U2 - 10.1016/j.physletb.2008.05.010

DO - 10.1016/j.physletb.2008.05.010

M3 - Article

AN - SCOPUS:44249093197

SN - 0370-2693

VL - 664

SP - 103

EP - 106

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

IS - 1-2

ER -