Breakdown of the linear approximation in the perturbative analysis of   heat conduction in relativistic systems
  We analyze the effects of thermal conduction in a relativistic fluid just after its departure from spherical symmetry, on a time scale of the order of relaxation time. Using first order perturbation theory, it is shown that, as in spherical systems, at a critical point the effective inertial mass density of a fluid element vanishes and becomes negative beyond that point. The impact of this effect on the reliability of causality conditions is discussed. 
L. Herrera, A. Di Prisco and J. Martinez