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Stability reversal in non-homogeneous static fluids inhigh-dimensional spaces

Gabriel Nagy
UCSD Department of Mathematics


Fluid models have been used as toy-models of event horizons in generalrelativity and its generalizations to more than four spacetime dimensions.We study here a fluid model for the Gregory-Laflamme instability in blackstrings. With consider a Newtonian, incompressible, static,axially-symmetric fluid with surface tension, in n dimensions plus oneperiodic dimension. The fluid configurations are those that minimize thefluid surface area for fixed volume. Homogeneous fluid configurations areknown to be stationary solutions of this functional, and they are stablein a dynamical sense above a critical value of the fluid volume. Belowthat value Plateau-Rayleigh instabilities occur. We show in this articlethat at this critical value of the volume there is a pitchfork bifurcationpoint. We prove that there are infinitely many other pitchfork bifurcationpoints at smaller values of the fluid volume. Each bifurcation solutionrepresents a non-homogeneous static fluid configuration and its stabilitydepends on the space dimension. By stability we mean in the sense ofminimum of the above functional. We show that the non-homogeneousconfigurations are all unstable if n less or equal 10, and they all becomestable if n bigger or equal 11. This stability inversion for high spacedimensions could be of interest in gravitational theories in more thanfour dimensions and in string theory.

Tuesday, October 10, 2006
11:00AM AP&M 2402