Rayleigh-Plateau and Gregory-Laflamme instabilities of black strings

Abstract

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 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 timescale is also well described within this model, as well as the dimensionality dependence. We conjecture that general non-axisymmetric perturbations are stable. We further argue that the instability of ultra-spinning black holes follows from this model.

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. Lett

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