Exact nonlinear solutions for three-dimensional Alfv\'en-wave packets in relativistic magnetohydrodynamics

TL;DR

This paper derives exact nonlinear solutions for large-amplitude Alfvén-wave packets in relativistic magnetohydrodynamics, showing they propagate without distortion and could be relevant in astrophysical relativistic outflows.

Contribution

It provides analytic solutions for constant-$b$ Alfvén waves in relativistic MHD, demonstrating their stability and potential astrophysical significance.

Findings

Large-amplitude AW packets are exact solutions when $b$ is constant.

These waves propagate at the relativistic Alfvén velocity without steepening.

Such waves are likely present in relativistic astrophysical outflows.

Abstract

We show that large-amplitude, non-planar, Alfv\'en wave (AW) packets are exact nonlinear solutions of the relativistic MHD equations when the total magnetic-field strength in the local fluid rest frame ($b$) is a constant. We derive analytic expressions relating the components of the fluctuating velocity and magnetic field. We also show that these constant-$b$ AWs propagate without distortion at the relativistic Alfv\'en velocity and never steepen into shocks. These findings and the observed abundance of large-amplitude, constant-$b$ AWs in the solar wind suggest that such waves may be present in relativistic outflows around compact astrophysical objects.