Causality of fluid dynamics for high-energy nuclear collisions

TL;DR

This paper investigates the conditions under which relativistic fluid dynamics in high-energy nuclear collisions remains causal, deriving inequalities that bound the applicability of fluid models based on causality principles.

Contribution

It provides a criterion for causality in relativistic fluid dynamics and discusses how initial conditions can violate this, impacting the validity of fluid models in nuclear collisions.

Findings

Derived a causality inequality for fluid evolution

Identified conditions where causality can be violated

Linked causality constraints to the applicability of fluid dynamics

Abstract

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. }