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We construct stationary non-equilibrium black funnels locally asymptotic toglobal AdS4 in vacuum Einstein-Hilbert gravity with negative cosmologicalconstant. These are non-compactly-generated black holes in which a singleconnected bulk horizon extends to meet the conformal boundary. Thus the induced(conformal) boundary metric has smooth horizons as well. In our examples, theboundary spacetime contains a pair of black holes connected through the bulk bya tubular bulk horizon. Taking one boundary black hole to be hotter than theother ($\Delta T \neq 0$) prohibits equilibrium. The result is a so-calledflowing funnel, a stationary bulk black hole with a non-Killing horizon thatmay be said to transport heat toward the cooler boundary black hole. Whilegenerators of the bulk future horizon evolve toward zero expansion in the farfuture, they begin at finite affine parameter with infinite expansion on asingular past horizon characterized by power-law divergences with universalexponents. We explore both the horizon generators and the boundary stresstensor in detail. While most of our results are numerical, a semi-analyticfluid/gravity description can be obtained by passing to a one-parametergeneralization of the above boundary conditions. The new parameter detunes thetemperatures $T_{bulk BH}$ and $T_{bndy BH}$ of the bulk and boundary blackholes, and we may then take \alpha = $T_\mathrm{bndy BH}/T_\mathrm{bulk BH}$and \Delta T small to control the accuracy of the fluid-gravity approximation.In the small \alpha, \Delta T regime we find excellent agreement with ournumerical solutions. For our cases the agreement also remains quite good evenfor $\alpha \sim 0.8$. In terms of a dual CFT, our \alpha = 1 solutionsdescribe heat transport via a large N version of Hawking radiation through adeconfined plasma that couples efficiently to both boundary black holes.

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