  It is shown that the coupling of heat with acceleration first proposed by
Eckart would have an overwhelming effect in the growth of density mass
fluctuations, even in non-relativistic fluids in the presence of a
gravitational field. Gravitational effects would be negligible if the
heat-acceleration relation is assumed to be valid for the hydrodynamic
equations. A direct implication of this result is that recent alternative first
order in the gradients theories must be taken into account while describing a
special relativistic fluid.
