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It is shown that the coupling of heat with acceleration first proposed byEckart would have an overwhelming effect in the growth of density massfluctuations, even in non-relativistic fluids in the presence of agravitational field. Gravitational effects would be negligible if theheat-acceleration relation is assumed to be valid for the hydrodynamicequations. A direct implication of this result is that recent alternative firstorder in the gradients theories must be taken into account while describing aspecial relativistic fluid.

Jeans instability analysis in the presence of heat in Eckart's frame