Exact solution of the hydrodynamical Riemann problem with nonzero tangential velocities and the ultrarelativistic equation of state

TL;DR

This paper provides an exact analytical solution to the relativistic hydrodynamical Riemann problem with nonzero tangential velocities under an ultrarelativistic equation of state, aiding numerical scheme development and testing.

Contribution

It presents the first exact analytical solution for the relativistic Riemann problem with tangential velocities and ultrarelativistic equation of state.

Findings

Analytical solution expressed in closed form.

Applicable to constructing and testing numerical schemes.

Simplifies the relativistic Riemann problem analysis.

Abstract

We give a solution of the Riemann problem in relativistic hydrodynamics in the case of ultrarelativistic equation of state and nonvanishing components of the velocity tangent to the initial discontinuity. Simplicity of the ultra-relativistic equation of state (the pressure being directly proportional to the energy density) allows us to express this solution in analytical terms. The result can be used both to construct and test numerical schemes for relativistic Euler equations in (3 + 1) dimensions.