We consider an accelerated relativistic fluid in four-dimensional (anti-)de
Sitter space-time. Analyzing only hydrodynamic equations, we construct the
equilibrium stress-energy tensor. We confirm that (A)dS vacuum corresponds to a
thermal bath in the accelerated frame with a temperature, depending on the
acceleration in a flat higher-dimensional (namely, five-dimensional) space, in
which curved space-times are embedded. We develop the duality between
hydrodynamics and gravity finding a direct relationship between the transport
coefficients in flat and curved space-times