A Novel Formula for Bulk Viscosity from the Null Horizon Focusing Equation

The null horizon focusing equation is equivalent via the fluid/gravity correspondence to the entropy balance law of the fluid. Using this equation we derive a simple novel formula for the bulk viscosity of the fluid. The formula is expressed in terms of the dependence of scalar fields at the horizon on thermodynamic variables such as the entropy and charge densities. We apply the formula to three classes of gauge theory plasmas: non-conformal branes, perturbations of the N=4 supersymmetric Yang-Mills theory and holographic models of QCD, and discuss its range of applicability.Comment: 23 pages, 1 appendi

The Anomalous Scaling Exponents of Turbulence in General Dimension from Random Geometry

We propose an exact analytical formula for the anomalous scaling exponents of inertial range structure functions in incompressible fluid turbulence. The formula is a gravitational Knizhnik-Polyakov-Zamolodchikov (KPZ)-type relation, and is valid in any number of space dimensions. It incorporates intermittency by gravitationally dressing the Kolmogorov linear scaling via a coupling to a random geometry. The formula has one real parameter $\gamma$ that depends on the number of space dimensions. The scaling exponents satisfy the convexity inequality, and the supersonic bound constraint. They agree with the experimental and numerical data in two and three space dimensions, and with numerical data in four space dimensions. Intermittency increases with $\gamma$, and in the infinite $\gamma$ limit the scaling exponents approach the value one, as in Burgers turbulence. At large $n$ the $n$th order exponent scales as $\sqrt{n}$. We discuss the relation between fluid flows and black hole geometry that inspired our proposal.Comment: 18 pages, 3 figures; v3: additional clarifications, added references; v2: improved discussion, added one figur

The Relativistic Rindler Hydrodynamics

We consider a (d+2)-dimensional class of Lorentzian geometries holographically dual to a relativistic fluid flow in (d+1) dimensions. The fluid is defined on a (d+1)-dimensional time-like surface which is embedded in the (d+2)-dimensional bulk space-time and equipped with a flat intrinsic metric. We find two types of geometries that are solutions to the vacuum Einstein equations: the Rindler metric and the Taub plane symmetric vacuum. These correspond to dual perfect fluids with vanishing and negative energy densities respectively. While the Rindler geometry is characterized by a causal horizon, the Taub geometry has a timelike naked singularity, indicating pathological behavior. We construct the Rindler hydrodynamics up to the second order in derivatives of the fluid variables and show the positivity of its entropy current divergence.Comment: 25 pages, 2 appendices; v3: improved presentation, corrected typo

Holographic Vorticity in the Fluid/Gravity Correspondence

The vorticity statistics characterises both the direct and the inverse turbulent cascades of two-dimensional fluid flows. The fluid/gravity correspondence relates fluid flows to black brane dynamics. We construct the holographic vorticity for relativistic and non-relativistic fluids in terms of the gravitational black brane data, and relate it to the horizon vorticity expressed as a Weyl scalar. We discuss the statistical scaling structure of the horizon geometry.Comment: 13 pages, v2: fixed typos, minor improvement

Horava-Lifshitz Black Hole Hydrodynamics

We consider the holographic hydrodynamics of black holes in generally covariant gravity theories with a preferred time foliation. Gravitational perturbations in these theories have spin two and spin zero helicity modes with generically different speeds. The black hole solutions possess a spacelike causal boundary called the universal horizon. We relate the flux of the spin zero perturbation across the universal horizon to the new dissipative transport in Lifshitz field theory hydrodynamics found in arXiv:1304.7481. We construct in detail the hydrodynamics of one such black hole solution, and calculate the ratio of the shear viscosity to the entropy density.Comment: 22 pages; v2: corrected final value of \eta/s, minor clarifications, fixed typos, added reference

Numerical simulations of gravitational collapse in Einstein-aether theory

We study gravitational collapse of a spherically symmetric scalar field in Einstein-aether theory (general relativity coupled to a dynamical unit timelike vector field). The initial value formulation is developed, and numerical simulations are performed. The collapse produces regular, stationary black holes, as long as the aether coupling constants are not too large. For larger couplings a finite area singularity occurs. These results are shown to be consistent with the stationary solutions found previously.Comment: 9 pages, 7 figures; v2: corrected typos, added minor clarifying remarks, improved discussion of results in conclusio