  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.
