  Dissipative relativistic fluid dynamics is not always causal and can favor
superluminal signal propagation under certain circumstances. On the other hand,
high-energy nuclear collisions have a microscopic description in terms of QCD
and are expected to follow the causality principle of special relativity. We
discuss under which conditions the fluid evolutions for a radial expansion are
hyperbolic and how the properties of the solutions are encoded in the
associated characteristic curves. The expansion dynamics is causal in
relativistic sense if the characteristic velocities are smaller than the speed
of light. We obtain a concrete inequality from this constraint and discuss how
it can be violated for certain initial conditions. We argue that causality
poses a bound to the applicability of relativistic fluid dynamics. }
