Black Holes as Incompressible Fluids on the Sphere

We consider finite deformations of the p+2-dimensional Schwarzschild geometry which obey the vacuum Einstein equation, preserve the mean curvature and induced conformal metric on a sphere a distance $\lambda$ from the horizon and are regular on the future horizon. We show perturbatively that in the limit $\lambda$ approaches 0 the deformations are given by solutions of the nonlinear incompressible Navier-Stokes equation on the p-sphere. This relation provides a link between global existence for p-dimensional incompressible Navier-Stokes fluids and a novel form of cosmic censorship in p+2-dimensional general relativity

Modeling microscopic swimmers at low Reynolds number

We employ three numerical methods to explore the motion of low Reynolds number swimmers, modeling the hydrodynamic interactions by means of the Oseen tensor approximation, lattice Boltzmann simulations and multiparticle collision dynamics. By applying the methods to a three bead linear swimmer, for which exact results are known, we are able to compare and assess the effectiveness of the different approaches. We then propose a new class of low Reynolds number swimmers, generalized three bead swimmers that can change both the length of their arms and the angle between them. Hence we suggest a design for a microstructure capable of moving in three dimensions. We discuss multiple bead, linear microstructures and show that they are highly efficient swimmers. We then turn to consider the swimming motion of elastic filaments. Using multiparticle collision dynamics we show that a driven filament behaves in a qualitatively similar way to the micron-scale swimming device recently demonstrated by Dreyfus et al.Comment: 12 pages, 10 figure

Black Hole Superradiance From Kerr/CFT

The superradiant scattering of a scalar field with frequency and angular momentum (w,m) by a near-extreme Kerr black hole with mass and spin (M, J) was derived in the seventies by Starobinsky, Churilov, Press and Teukolsky. In this paper we show that for frequencies scaled to the superradiant bound the full functional dependence on (w,m,M, J) of the scattering amplitudes is precisely reproduced by a dual twodimensional conformal field theory in which the black hole corresponds to a specific thermal state and the scalar field to a specific operator. This striking agreement corroborates a conjectured Kerr/CFT correspondence.Physic

Incompressible Fluids of the de Sitter Horizon and Beyond

There are (at least) two surfaces of particular interest in eternal de Sitter space. One is the timelike hypersurface constituting the lab wall of a static patch observer and the other is the future boundary of global de Sitter space. We study both linear and non-linear deformations of four-dimensional de Sitter space which obey the Einstein equation. Our deformations leave the induced conformal metric and trace of the extrinsic curvature unchanged for a fixed hypersurface. This hypersurface is either timelike within the static patch or spacelike in the future diamond. We require the deformations to be regular at the future horizon of the static patch observer. For linearized perturbations in the future diamond, this corresponds to imposing incoming flux solely from the future horizon of a single static patch observer. When the slices are arbitrarily close to the cosmological horizon, the finite deformations are characterized by solutions to the incompressible Navier-Stokes equation for both spacelike and timelike hypersurfaces. We then study, at the level of linearized gravity, the change in the discrete dispersion relation as we push the timelike hypersurface toward the worldline of the static patch. Finally, we study the spectrum of linearized solutions as the spacelike slices are pushed to future infinity and relate our calculations to analogous ones in the context of massless topological black holes in AdS$_4$.Comment: 27 pages, 8 figure

Cargese Lectures on the Kerr/CFT Correspondence

We give a short introduction, beginning with the Kerr geometry itself, to the basic results, motivation, open problems and future directions of the Kerr/CFT correspondence.Comment: Lectures given by A. Strominger at Cargese 2010. References update

Wilsonian Approach to Fluid/Gravity Duality

The problem of gravitational fluctuations confined inside a finite cutoff at radius $r=r_c$ outside the horizon in a general class of black hole geometries is considered. Consistent boundary conditions at both the cutoff surface and the horizon are found and the resulting modes analyzed. For general cutoff $r_c$ the dispersion relation is shown at long wavelengths to be that of a linearized Navier-Stokes fluid living on the cutoff surface. A cutoff-dependent line-integral formula for the diffusion constant $D(r_c)$ is derived. The dependence on $r_c$ is interpreted as renormalization group (RG) flow in the fluid. Taking the cutoff to infinity in an asymptotically AdS context, the formula for $D(\infty)$ reproduces as a special case well-known results derived using AdS/CFT. Taking the cutoff to the horizon, the effective speed of sound goes to infinity, the fluid becomes incompressible and the Navier-Stokes dispersion relation becomes exact. The resulting universal formula for the diffusion constant $D(horizon)$ reproduces old results from the membrane paradigm. Hence the old membrane paradigm results and new AdS/CFT results are related by RG flow. RG flow-invariance of the viscosity to entropy ratio $\eta /s$ is shown to follow from the first law of thermodynamics together with isentropy of radial evolution in classical gravity. The ratio is expected to run when quantum gravitational corrections are included.Comment: 34 pages, harvmac, clarified boundary conditio

Lymphocyte and monocyte flow cytometry immunophenotyping as a diagnostic tool in uncharacteristic inflammatory disorders

<p>Abstract</p> <p>Background</p> <p>Patients with uncharacteristic inflammatory symptoms such as long-standing fatigue or pain, or a prolonged fever, constitute a diagnostic and therapeutic challenge. The aim of the present study was to determine if an extended immunophenotyping of lymphocytes and monocytes including activation markers can define disease-specific patterns, and thus provide valuable diagnostic information for these patients.</p> <p>Methods</p> <p>Whole blood from patients with gram-negative bacteraemia, neuroborreliosis, tuberculosis, acute mononucleosis, influenza or a mixed connective tissue disorders, as diagnosed by routine culture and serology techniques was analysed for lymphocyte and monocyte cell surface markers using a no-wash, no-lyse protocol for multi-colour flow cytometry method. The immunophenotyping included the activation markers HLA-DR and CD40. Plasma levels of soluble TNF alpha receptors were analysed by ELISA.</p> <p>Results</p> <p>An informative pattern was obtained by combining two of the analysed parameters: (i), the fractions of HLA-DR-expressing CD4+ T cells and CD8+ T cells, respectively, and (ii), the level of CD40 on CD14+ CD16- monocytes. Patients infected with gram-negative bacteria or EBV showed a marked increase in monocyte CD40, while this effect was less pronounced for tuberculosis, borrelia and influenza. The bacterial agents could be distinguished from the viral agents by the T cell result; CD4+ T cells reacting in bacterial infection, and the CD8+ T cells dominating for the viruses. Patients with mixed connective tissue disorders also showed increased activation, but with similar engagement of CD4+ and CD8+ T cells. Analysis of soluble TNF alpha receptors was less informative due to a large inter-individual variation.</p> <p>Conclusion</p> <p>Immunophenotyping including the combination of the fractions of HLA-DR expressing T cell subpopulations with the level of CD40 on monocytes produces an informative pattern, differentiating between infections of bacterial and viral origin. Furthermore, a quantitative analysis of these parameters revealed the novel finding of characteristic patterns indicating a subacute bacterial infection, such as borreliosis or tuberculosis, or a mixed connective tissue disorder. The employed flow cytometric method is suitable for clinical diagnostic laboratories, and may help in the assessment of patients with uncharacteristic inflammatory symptoms.</p

From Navier-Stokes To Einstein

We show by explicit construction that for every solution of the incompressible Navier-Stokes equation in $p+1$ dimensions, there is a uniquely associated "dual" solution of the vacuum Einstein equations in $p+2$ dimensions. The dual geometry has an intrinsically flat timelike boundary segment $\Sigma_c$ whose extrinsic curvature is given by the stress tensor of the Navier-Stokes fluid. We consider a "near-horizon" limit in which $\Sigma_c$ becomes highly accelerated. The near-horizon expansion in gravity is shown to be mathematically equivalent to the hydrodynamic expansion in fluid dynamics, and the Einstein equation reduces to the incompressible Navier-Stokes equation. For $p=2$, we show that the full dual geometry is algebraically special Petrov type II. The construction is a mathematically precise realization of suggestions of a holographic duality relating fluids and horizons which began with the membrane paradigm in the 70's and resurfaced recently in studies of the AdS/CFT correspondence.Comment: 15 pages, 2 figures, typos correcte

The Einstein and the Navier-Stokes Equations: Connecting the Two

This thesis establishes a precise mathematical connection between the Einstein equations of general relativity and the incompressible Navier-Stokes equation of fluid dynamics. We carry out a holographic analysis which relates solutions to the Einstein equations to the behaviour of a dual fluid living in one fewer dimensions. Gravitational systems are found to exhibit Navier-Stokes behaviour when we study the dynamics of the region near an event horizon. Thus, we find non-linear deformations of Einstein solutions which, after taking a suitable near horizon limit and imposing our particular choice of boundary conditions, turn out to be precisely characterised by solutions to the incompressible Navier-Stokes equation. In other words, for any solution to the Navier-Stokes equation, the set-up we present provides a solution to the Einstein equations near a horizon. We consider the cases of fluids flowing on the plane and on the sphere. Fluid dynamics on the plane is analysed foremost in the context of a flat background geometry whilst the spherical analysis is undertaken for Schwarzschild black holes and the static patch of four-dimensional de Sitter space.Physic

A longitudinal cohort study on the prevalence of Helicobacter pylori antibodies in Swedish children and adolescents.

The aim of this study was to monitor the Helicobacter pylori antibody seroprevalence of an asymptomatic cohort between the ages of 4 and 18 y. The H. pylori antibody titres in a longitudinally followed cohort of 168 native Swedish children (born between 1972 and 1974) were established at 4, 8, 12, 16, and 18 y of age. Seventeen children (10.1%) were found positive on at least one occasion when a paediatric cut-off was applied. Five children (3.0%) reached levels considered positive in adults. The seroprevalence at 4 y of age was 4.0%, at 8 y 2.5%, at 12 y 4.9%, at 16 y 5.3%, and at 18 y 6.3%. The difference in serological titres between the age groups was not significant. A change from negative to positive after the age of 4 took place in 5 of the cases. Spontaneous seroreversion appeared in 5 cases. CONCLUSION: Our findings showed no significant differences among the various age groups. Seventeen of the 168 children (10.1%) had been infected at some time, the prevalence ranging from 2.5% to 6.3%. Seroconversion and seroreversion occurred infrequently between the ages of 4 and 18 y