275 research outputs found
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
D-brane Construction of the 5D NHEK Dual
Extremal but non-supersymmetric charged black holes with SU(2)_L spin in IIB
string theory compactified to five dimensions on K^3 x S^1 are considered.
These have a near-horizon or NHEK region with an enhanced SL(2,R)_L conformal
symmetry. It is shown that the NHEK geometry has a second, inequivalent,
asymptotically flat extension in which the radius of the S^1 becomes infinite
but the radius of the angular circles of SU(2)_L orbits approach a constant.
The asymptotic charges associated to the second solution identify it as a 5D
D1-D5-Taub-NUT black string with certain nonzero worldvolume charge densities,
temperatures and chemical potentials. The dual of the NHEK geometry is then
identified as an IR limit of this wrapped brane configuration.Comment: 11 page
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.Comment: 27 pages, 8 figure
Causality and the AdS Dirichlet problem
The (planar) AdS Dirichlet problem has previously been shown to exhibit
superluminal hydrodynamic sound modes. This problem is defined by bulk
gravitational dynamics with Dirichlet boundary conditions imposed on a rigid
timelike cut-off surface. We undertake a careful examination of this set-up and
argue that, in most cases, the propagation of information between points on the
Dirichlet hypersurface is nevertheless causal with respect to the induced light
cones. In particular, the high-frequency dynamics is causal in this sense.
There are however two exceptions and both involve boundary gravitons whose
propagation is not constrained by the Einstein equations. These occur in i)
AdS, where the boundary gravitons generally do not respect the induced
light cones on the boundary, and ii) Rindler space, where they are related to
the infinite speed of sound in incompressible fluids. We discuss implications
for the fluid/gravity correspondence with rigid Dirichlet boundaries and for
the black hole membrane paradigm.Comment: 29 pages, 5 figures. v2: added refs. v3: minor clarification
Connecting the Holographic and Wilsonian Renormalization Groups
Inspired by the AdS/CFT correspondence, we develop an explicit formal duality
between the planar limit of a d-dimensional gauge theory and a classical field
theory in a (d+1)-dimensional anti-de Sitter space. The key ingredient is the
identification of fields in AdS with generalized Hubbard-Stratonovich
transforms of single-trace couplings of the QFT. We show that the Wilsonian
renormalization group flow of these transformed couplings matches the
holographic (Hamilton-Jacobi) flow of bulk fields along the radial direction in
AdS. This result allows one to outline an AdS/CFT dictionary that does not rely
on string theory.Comment: 11 pages, 1 figure; metadata modified in v2; added references and
minor changes in v3; v4 as published in JHE
Hidden Conformal Symmetry of Extremal Kerr-Bolt Spacetimes
We show that extremal Kerr-Bolt spacetimes have a hidden conformal symmetry.
In this regard, we consider the wave equation of a massless scalar field
propagating in extremal Kerr-Bolt spacetimes and find in the "near region", the
wave equation in extremal limit can be written in terms of the
quadratic Casimir. Moreover, we obtain the microscopic entropy of the extremal
Kerr-Bolt spacetimes also we calculate the correlation function of a
near-region scalar field and find perfect agreement with the dual 2D CFT.Comment: 13 page
On the Stress Tensor of Kerr/CFT
The recently-conjectured Kerr/CFT correspondence posits a field theory dual
to dynamics in the near-horizon region of an extreme Kerr black hole with
certain boundary conditions. We construct a boundary stress tensor for this
theory via covariant phase space techniques. The structure of the stress tensor
indicates that any dual theory is a discrete light cone quantum theory, in
agreement with recent arguments by Balasubramanian et al. The key technical
step in our construction is the addition of an appropriate counter-term to the
symplectic structure, which is necessary to make the theory fully covariant and
to resolve a subtle problem involving the integrability of charges.Comment: 19 page
Near Extremal Kerr Entropy from AdS_2 Quantum Gravity
We analyze the asymptotic symmetries of near extremal Kerr black holes in
four dimensions using the AdS_2/CFT_1 correspondence. We find a Virasoro
algebra with central charge c_R=12J that is independent from the Virasoro
algebra (with the same central charge) that acts on the degenerate ground
state. The energy of the excitations is computed as well, and we can use
Cardy's formula to determine the near extremal entropy. Our result is
consistent with the Bekenstein-Hawking area law for near extremal Kerr black
holes.Comment: 28 pages. v2: references added, typos correcte
Yet Another Realization of Kerr/CFT Correspondence
The correspondence between the Kerr black hole and a boundary CFT has been
conjectured recently. The conjecture has been proposed first only for the half
of the CFT, namely for left movers. For right movers, the correspondence has
been also found out through the suitable asymptotic boundary condition.
However, the boundary conditions for these two studies are exclusive to each
other. The boundary condition for left movers does not allow the symmetry of
right movers, and vice versa. We propose new boundary condition which allows
both of left and right movers.Comment: 6 pages, references adde
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