Black Funnels

The Hartle-Hawking state of N=4 SYM at strong coupling and large N on a fixed black hole background has two proposed gravitational duals: a black funnel or a black droplet. We construct the black funnel solutions that are dual to the Hartle-Hawking state on a Schwarzschild black hole and on a class of three-dimensional asymptotically flat black hole backgrounds. We compute their holographic stress tensor and argue for the stability of these solutions.