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
