2008/04/30 by Umpei Miyamoto
Engineering · Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Fluid Dynamics and Turbulent Flows #gr-qc #hep-th #math-ph #math.MP #physics.flu-dyn
paper · pdf · doi:10.1103/physrevd.78.026001
published as Phys.Rev.D78:026001,2008 · 14 pages, 5 figures; v2: references added, typos fixed
arxiv created 2008/05/29 · openalex publication_date 2008/07/07 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
It can be expected that the respective endpoints of the Gregory-Laflamme black brane instability and the Rayleigh-Plateau membrane instability are related because the bifurcation diagrams of the black hole--black string system and the liquid drop--liquid bridge system display many similarities. In this paper, I investigate the nonlinear dynamics of the Rayleigh-Plateau instability in a range of dimensions, including the critical dimension at which the phase structure changes. I show that near the critical dimension and above, depending on a parameter in initial conditions an unstable cylinder will either pinch off or converge to an equilibrium state. The equilibrium state is apparently nonuniform but has a constant mean curvature everywhere. The results suggest that in the gravity side, near the critical dimension and above, the final state of an unstable black string (which is not too long) is a nonuniform black string. The equation of motion adopted to describe the dynamics is the surface diffusion equation, which was originally proposed to describe a grooving process of heated metal surfaces. An interesting correspondence between the diffusion dynamics and black hole (thermo)dynamics is discussed.