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Black String Flow

We give an exact description of the steady flow of a black string into a planar horizon. The event horizon is out of equilibrium and provides a simple, exact instance of a `flowing black funnel' in any dimension D>=5. It is also an approximation to a smooth intersection between a black string and a black hole, in the limit in which the black hole is much larger than the black string thickness. The construction extends easily to more general flows, in particular charged flows.