Christopher Eling, Adiel Meyer, Yaron Oz
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
viscous order and show the positivity of its entropy current divergence.
View original:
http://arxiv.org/abs/1201.2705
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