Correspondence between Israel-Stewart and first-order causal and stable hydrodynamics for Bjorken-expanding baryon-rich systems with vanishing particle masses

TL;DR

This paper establishes an exact mathematical link between Israel-Stewart and first-order causal hydrodynamics for baryon-rich, boost-invariant systems, revealing stability conditions and differences in their dynamical equations.

Contribution

It provides explicit formulas connecting Israel-Stewart and FOCS hydrodynamics, and demonstrates the instability of Israel-Stewart theory under certain conditions.

Findings

Derived explicit relations between IS and FOCS theories.

Applied FOCS stability conditions to IS theory.

Found that the IS theory considered is unstable.

Abstract

We obtain an exact correspondence between the dynamical equations in Israel-Stewart (IS) theory and first-order causal and stable (FOCS) hydrodynamics for a boost-invariant system with an ideal gas equation of state at finite baryon chemical potential. Explicit expressions for the temperature and chemical potential dependence of the regulators in the FOCS theory are given in terms of the kinetic coefficients and constant relaxation time of the IS theory. Using the correspondence between the IS and FOCS theory, stability conditions for a charged fluid which are known in the FOCS approach are applied and one finds that the IS theory considered is unstable.