We describe the behavior of a perturbed 5-dimensional black string subject to
the Gregory-Laflamme instability. We show that the horizon evolves in a
self-similar manner, where at any moment in the late-time development of the
instability the horizon can be described as a sequence of 3-dimensional
spherical black holes of varying size, joined by black string segments of
similar radius. As with the initial black string, each local string segment is
itself unstable, and this fuels the self-similar cascade to (classically)
arbitrarily small scales; in the process the horizon develops a fractal
structure. In finite asymptotic time, the remaining string segments shrink to
zero-size, yielding a naked singularity. Since no fine-tuning is required to
excite the instability, this constitutes a generic violation of cosmic
censorship. We further discuss how this behavior is related to satellite
formation in low-viscosity fluid streams subject to the Rayleigh-Plateau
instability, and estimate the fractal dimension of the horizon prior to
formation of the naked singularity.Comment: 27 pages, 6 Figures. Chapter of the book `Black Holes in Higher
Dimensions' to be published by Cambridge University Press (editor: G.
Horowitz