Maxwell-Cattaneo's equation and the stability of fluctuations in the   relativistic fluid
  Extended theories are widely used in the literature to describe the relativistic fluid. The motivation for this is mostly due to the causality issues allegedly present in the first order theories. However, the decay of fluctuations in the system is also at stake when first order theories \emph{that couple heat with acceleration} are used. In this paper it is shown how the generic instabilities in relativistic fluids are not present when a Maxwell-Cattaneo type law is introduced in the system of hydrodynamic equations. Emphasis is made on the fact that the stabilization is only due to the difference in characteristic times for heat flux relaxation and instabilities onset. This gives further evidence that Eckart's like constitutive equations are responsible for the first order sytem exhibiting unphysical behavior. 
D. Brun-Battistini, A. Sandoval-Villalbazo and A. L. Garcia-Perciante
gr-qc cond-mat.stat-mech