AdS flowing black funnels: Stationary AdS black holes with non-Killing horizons and heat transport in the dual CFT

We construct stationary non-equilibrium black funnels locally asymptotic to global AdS${}_4$ in vacuum Einstein-Hilbert gravity with negative cosmological constant. These are non-compactly-generated black holes in which a single connected bulk horizon extends to meet the conformal boundary. Thus the induced (conformal) boundary metric has smooth horizons as well. In our examples, the boundary spacetime contains a pair of black holes connected through the bulk by a tubular bulk horizon. Taking one boundary black hole to be hotter than the other ($\Delta T \neq 0$) prohibits equilibrium. The result is a so-called flowing funnel, a stationary bulk black hole with a non-Killing horizon that may be said to transport heat toward the cooler boundary black hole. While most of our results are numerical, a semi-analytic fluid/gravity description can be obtained by passing to a one-parameter generalization of the above boundary conditions. In the fluid regime, we find excellent agreement with our numerical solutions. In terms of a dual CFT, our solutions describe heat transport via a large $N$ version of Hawking radiation through a deconfined plasma that couples efficiently to both boundary black holes.