# Modification of magnetohydrodynamic waves by the relativistic Hall effect

## TL;DR

This paper investigates how the relativistic Hall effect alters wave propagation in magnetohydrodynamics, revealing bounds on anisotropy and dependencies on plasma parameters, which differ from non-relativistic predictions.

## Contribution

It derives a linear dispersion relation for relativistic Hall MHD and uncovers how relativistic effects modify wave anisotropy and characteristic scale lengths.

## Key findings

- Relativistic Hall effect bounds wave anisotropy.
- Group velocities of Alfvén and fast waves coalesce into a single surface.
- Characteristic scale length depends on ion temperature, magnetic field, and density.

## Abstract

This study shows that a relativistic Hall effect significantly changes the properties of wave propagation by deriving a linear dispersion relation for relativistic Hall magnetohydrodynamics (HMHD). Whereas, in non- relativistic HMHD, the phase and group velocities of fast magnetosonic wave become anisotropic with an increasing Hall effect, the relativistic Hall effect brings upper bounds to the anisotropies. The Alfve\'en wave group velocity with strong Hall effect also becomes less anisotropic than non-relativistic case. Moreover, the group velocity surfaces of Alfv\'en and fast waves coalesce into a single surface in the direction other than near perpendicular to the ambient magnetic field. It is also remarkable that a characteristic scale length of the relativistic HMHD depends on ion temperature, magnetic field strength, and density while the non-relativistic HMHD scale length, i.e., ion skin depth, depends only on density. The modified characteristic scale length increases as the ion temperature increases and decreases as the magnetic field strength increases.