Analytical solutions of causal relativistic hydrodynamic equations for Bjorken and Gubser flows

TL;DR

This paper derives analytical solutions for third-order viscous hydrodynamics in relativistic systems with Bjorken and Gubser flows, characterizing hydrodynamic attractors and their properties.

Contribution

It provides the first general analytical solutions for third-order viscous hydrodynamics in these flow scenarios, including the analysis of hydrodynamic attractors.

Findings

Analytical solutions for third-order viscous hydrodynamics in Bjorken and Gubser flows.

Characterization of hydrodynamic attractors at early and late times.

Properties of attractors derived from kinetic theory with relaxation-time approximation.

Abstract

We obtain general analytical solutions of third-order viscous hydrodynamic equations for Bjorken and Gubser flows in systems with vanishing bulk viscosity and chemical potential, and having a constant shear relaxation time. We also analytically characterize and determine the hydrodynamic attractors for such systems by studying the universal behavior of these solutions at both early and late times. Finally we study the properties of these hydrodynamic attractors for transport coefficients obtained from relativistic kinetic theory in the relaxation-time approximation.