On freeze-out problem in relativistic hydrodynamics

TL;DR

This paper examines the relativistic freeze-out problem in hydrodynamics, highlighting the frame-dependence of equilibrium and proposing alternative methods to the traditional Cooper--Frye approach to ensure energy-momentum conservation.

Contribution

It reveals the non-uniqueness of the Cooper--Frye freeze-out recipe and discusses alternative approaches that satisfy conservation laws.

Findings

The Cooper--Frye method is not unique and can violate conservation laws.

Alternative freeze-out recipes can better satisfy energy-momentum conservation.

Frame dependence affects the equilibrium status in relativistic systems.

Abstract

A finite unbound system which is equilibrium in one reference frame is in general nonequilibrium in another frame. This is a consequence of the relative character of the time synchronization in the relativistic physics. This puzzle was a prime motivation of the Cooper--Frye approach to the freeze-out in relativistic hydrodynamics. Solution of the puzzle reveals that the Cooper--Frye recipe is far not a unique phenomenological method that meets requirements of energy-momentum conservation. Alternative freeze-out recipes are considered and discussed.