Correspondence between Israel-Stewart and first-order casual and stable hydrodynamics for the boost-invariant massive case with zero baryon density

TL;DR

This paper establishes an exact correspondence between Israel-Stewart and first-order causal hydrodynamics for a boost-invariant massive gas, providing explicit regulators and analyzing stability and causality conditions.

Contribution

It demonstrates the precise relationship between Israel-Stewart and first-order hydrodynamics in a specific relativistic setting, including explicit regulator expressions.

Findings

Exact correspondence established for the massive case.

Explicit temperature-dependent regulators derived.

Identified violation of a known stability condition.

Abstract

Exact correspondence between Israel-Stewart theory and first-order causal and stable hydrodynamics is established for the boost-invariant massive case with zero baryon density and the same constant relaxation times used in the shear and bulk sectors. Explicit expressions for the temperature dependent regulators are given for the case of a relativistic massive gas. The stability and causality conditions known in the first-order approach are applied and one finds that one of them is violated in this case.