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

TL;DR

This paper constructs stationary, non-equilibrium AdS black funnel solutions with non-Killing horizons, modeling heat transport in the dual conformal field theory, and explores their properties through numerical and semi-analytic methods.

Contribution

It introduces new stationary black funnel solutions with non-Killing horizons in AdS4 and analyzes heat transport in the dual CFT using both numerical and fluid/gravity approaches.

Findings

Black funnel solutions with non-Killing horizons are constructed.

Heat transport modeled by these solutions matches fluid/gravity predictions.

Solutions exhibit universal horizon behavior and detailed stress tensor analysis.

Abstract

We construct stationary non-equilibrium black funnels locally asymptotic to global AdS4 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 generators of the bulk future horizon evolve toward zero expansion in the far future, they begin at finite affine parameter with infinite expansion on a singular past horizon characterized by power-law divergences with universal exponents. We explore both the horizon generators and the boundary stress tensor in detail. 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. The new parameter detunes the temperatures $T_{bulk BH}$ and $T_{bndy BH}$ of the bulk and boundary black holes, 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 our numerical solutions. For our cases the agreement also remains quite good even for $\alpha \sim 0.8$. In terms of a dual CFT, our \alpha = 1 solutions describe heat transport via a large N version of Hawking radiation through a deconfined plasma that couples efficiently to both boundary black holes.