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

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.

Corrections according to the version published in Phys. Rev. E

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• Rotating Stars in Relativity
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• A powerful hydrodynamic booster for relativistic jets
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