Curvature driven diffusion, Rayleigh-Plateau, and Gregory-Laflamme

Understand

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, we investigate the non-linear dynamics of the Rayleigh-Plateau instability in a range of dimensions, including the critical dimension at which the phase structure changes.
• We 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 non-uniform but has a constant mean curvature everywhere.