Projection method for boost-invariant and cylindrically symmetric dissipative hydrodynamics

TL;DR

This paper introduces a projection method to simplify the equations governing boost-invariant, cylindrically symmetric dissipative relativistic fluids, connecting early and late-stage hydrodynamic models in heavy-ion collisions.

Contribution

It develops a projection-based approach to derive scalar equations for relativistic dissipative hydrodynamics, unifying early anisotropic and later near-equilibrium descriptions.

Findings

Simplified scalar equations for dissipative hydrodynamics

Matching conditions between ADHYDRO and Israel-Stewart models

Application to heavy-ion collision evolution

Abstract

Tensors describing boost-invariant and cylindrically symmetric expansion of a relativistic dissipative fluid are decomposed in a suitable chosen basis of projection operators. This leads to a simple set of scalar equations which determine the fluid behavior. As special examples, we discuss the case of the Israel-Stewart theory and the model of highly-anisotropic and strongly-dissipative hydrodynamics ADHYDRO. We also introduce the matching conditions between the ADHYDRO description suitable for the very early stages of heavy-ion collisions and the Israel-Stewart theory applicable for later stages when the system is close to equilibrium.