Relativistic dissipative hydrodynamics with extended matching conditions for ultra-relativistic heavy-ion collisions

TL;DR

This paper extends a relativistic dissipative hydrodynamics framework to arbitrary Lorentz frames, ensuring stability and causality, and applies it to ultra-relativistic heavy-ion collisions, confirming sound speed constraints for stability.

Contribution

It generalizes the extended matching conditions formalism to arbitrary Lorentz frames and analyzes stability and causality in the Landau frame for heavy-ion collision fluids.

Findings

Linearized equations are stable against small perturbations.

Fluid stability requires sound speed to be less than the speed of light.

The stability conditions align with previous Eckart frame results.

Abstract

Recently we proposed a novel approach to the formulation of relativistic dissipative hydrodynamics by extending the so-called matching conditions in the Eckart frame [Phys. Rev. {\bf C 85}, (2012) 14906]. We extend this formalism further to the arbitrary Lorentz frame. We discuss the stability and causality of solutions of fluid equations which are obtained by applying this formulation to the Landau frame, which is more relevant to treat the fluid produced in ultra-relativistic heavy-ion collisions. We derive equations of motion for a relativistic dissipative fluid with zero baryon chemical potential and show that linearized equations obtained from them are stable against small perturbations. It is found that conditions for a fluid to be stable against infinitesimal perturbations are equivalent to imposing restrictions that the sound wave, $c_s$, propagating in the fluid, must not exceed the speed of light $c$, i.e., $c_s < c$. This conclusion is equivalent to that obtained in the previous paper using the Eckart frame [Phys. Rev. {\bf C 85}, (2012) 14906].