Rayleigh-Plateau and Gregory-Laflamme Instabilities of Black Strings

Many and very general arguments indicate that the event horizon behaves as a stretched membrane. We explore this analogy by associating the Gregory-Laflamme instability of black strings with a classical membrane instability known as the Rayleigh-Plateau instability. We show that the key features of the black string instability can be reproduced using this viewpoint. In particular, we get good agreement for the threshold mode in all dimensions and exact agreement for large spacetime dimensionality. The instability time scale is also well described within this model, as well as the dimensionality dependence. It also predicts that general nonaxisymmetric perturbations are stable. We further argue that the instability of ultraspinning black holes follows from this model.

Figure 1

Black strings and fluid cylinders are unstable to perturbations on the extended dimension, i.e., along the axis of the cylinder. Ripples propagating along this axis grow exponentially with time for wavelengths of order of the radius of the cylinder.

Figure 2

Rayleigh-Plateau instability of a hyper-cylinder in several dimensions. Here the effective surface tension and density were chosen to match those of a higher-dimensional nonrotating black hole.