Relativistic Hydrodynamics and Non-Equilibrium Steady States

TL;DR

This paper reviews the relativistic Riemann problem as a tool for creating non-equilibrium steady states, comparing new double shock solutions with older solutions, and exploring effects of nonlinear deformations on system properties.

Contribution

It introduces and compares new double shock solutions with traditional ones in the relativistic Riemann problem and examines the impact of nonlinear deformations on steady states.

Findings

Older solutions with one shock and one rarefaction wave are preferred in simulations.

Double shock solutions are a theoretical alternative but less favored.

Nonlinear deformations influence temperature and velocity profiles in the connecting region.

Abstract

We review recent interest in the relativistic Riemann problem as a method for generating a non-equilibrium steady state. In the version of the problem under con- sideration, the initial conditions consist of a planar interface between two halves of a system held at different temperatures in a hydrodynamic regime. The new double shock solutions are in contrast with older solutions that involve one shock and one rarefaction wave. We use numerical simulations to show that the older solutions are preferred. Briefly we discuss the effects of a conserved charge. Finally, we discuss deforming the relativistic equations with a nonlinear term and how that deformation affects the temperature and velocity in the region connecting the asymptotic fluids.