Linear wave propagation in relativistic magnetohydrodynamics

TL;DR

This paper analyzes the properties of linear Alfvén, slow, and fast magnetoacoustic waves in relativistic MHD, providing phase and group speed diagrams to visualize anisotropic wave behavior and relativistic effects, useful for benchmarking numerical algorithms.

Contribution

It extends classical MHD wave analysis to relativistic regimes using a 3+1 formalism and graphical methods, including aberration effects and benchmarking tools.

Findings

Graphical phase and group speed diagrams for relativistic MHD waves

Confirmation of classical Huygens construction in relativistic context

Benchmark formulas for numerical relativistic MHD simulations

Abstract

The properties of linear Alfv\'en, slow, and fast magnetoacoustic waves for uniform plasmas in relativistic magnetohydrodynamics (MHD) are discussed, augmenting the well-known expressions for their phase speeds with knowledge on the group speed. A 3+1 formalism is purposely adopted to make direct comparison with the Newtonian MHD limits easier and to stress the graphical representation of their anisotropic linear wave properties using the phase and group speed diagrams. By drawing these for both the fluid rest frame and for a laboratory Lorentzian frame which sees the plasma move with a three-velocity having an arbitrary orientation with respect to the magnetic field, a graphical view of the relativistic aberration effects is obtained for all three MHD wave families. Moreover, it is confirmed that the classical Huygens construction relates the phase and group speed diagram in the usual way, even for the lab frame viewpoint. Since the group speed diagrams correspond to exact solutions for initial conditions corresponding to a localized point perturbation, their formulae and geometrical construction can serve to benchmark current high-resolution algorithms for numerical relativistic MHD.