Rayleigh-Plateau and Gregory-Laflamme Instabilities of Black Strings

Many and very general arguments indicate that the event horizon behaves as astretched membrane. We explore this analogy by associating the Gregory-Laflammeinstability of black strings with a classical membrane instability known asRayleigh-Plateau instability. We show that the key features of the black stringinstability can be reproduced using this viewpoint. In particular, we get goodagreement for the threshold mode in all dimensions and exact agreement forlarge spacetime dimensionality. The instability timescale is also welldescribed within this model, as well as the dimensionality dependence. Weconjecture that general non-axisymmetric perturbations are stable. We furtherargue that the instability of ultra-spinning black holes follows from thismodel.Comment: 4 pages, 2 Figures. RevTex4. v2: Added section discussing the existence of a critical dimension also in the fluid model. v3: Added discussion on breakup time, plot of instability corrected (now much more similar to G-L). Version to appear in Phys. Rev. Let