Causality of fluid dynamics for high-energy nuclear collisions

Abstract

Dissipative relativistic fluid dynamics is not always causal and can favor super-luminal 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 evolution equations for a radial expansion are hyperbolic and that terms of second order in the Knudsen number are problematic for causality. We also outline briefly how this can be remedied with terms of higher order in a formal derivative expansion. The expansion dynamics are causal in the 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. Finally we argue that causality poses a bound on the applicability of relativistic fluid dynamics.