Black funnels and droplets from the AdS C-metrics

Abstract

We recently argued that the dynamics of strongly coupled field theories in black hole backgrounds is related via the AdS/CFT correspondence to two new classes of AdS black hole solutions: black funnels, and black droplets suspended above a second disconnected horizon. The funnel solutions are dual to black holes coupling strongly to a field theory plasma. In contrast, the droplet solutions describe black holes coupling only weakly. We continue our investigation of these solutions and construct a wide variety of examples from the AdS C-metric in four bulk spacetime dimensions. The solutions we find are dual to field theories on spatially compact universes with Killing horizons.

Figures (7)

• Figure 1: A sketch of our two novel classes of solutions: (a): black funnel and (b): black droplet above a deformed planar black hole.
• Figure 2: We plot the functions $F(x)$ and $G(x)$ for various values of $\lambda$ with the different panels corresponding to varying $\mu$ and $\kappa$ as indicated under the respective plots. The solid curve is the function $G(x)$ while the dashed curves correspond to $F(x)$ which are plotted for various values of $\lambda$ (which corresponds to the value of $F(0)$). The lowest (dot-dashed) curve has the limiting value $\lambda = -1$.
• Figure 3: A plot of the domains in the $\{\lambda, \mu\}$ plane which characterize the distinct possibilities for the root structure of $F(\xi)$ and $G(\xi)$ for $\kappa =1$. The behavior of $G(\xi)$ is simply controlled by the parameter $\mu$, while $F(\xi)$ has non-trivial behavior across the various domains as indicated. See main text for a detailed explanation.
• Figure 4: A sketch of the possible coordinate domains for the AdS C-metric with $\kappa =1$ for various values of $\mu$. Horizons (diagonal lines) are plotted in the $(x,z)$ plane. Note that $z$ increases downward while $x$ increases to the right. The allowed regions are indicated by the roman numerals and can be considered as a complete spacetime unto themselves. To maintain the correct Lorentz signature, the allowed regions are $x \le x_0$ and $x \in [x_1,x_2]$ respectively which are indicated by the numbers. The different panels for a given value of $\mu$ correspond to situations with different numbers of roots for $F(x)$; for a detailed behavior of the roots see Fig. \ref{['f:fgplots']}.
• Figure 5: A sketch of the possible coordinate domains for the AdS C-metric with $\kappa =0$. Same conventions are used here as in Fig. \ref{['f:regionk1']}.