# Wave dispersion in pulsar plasma: 2. Pulsar frame

## TL;DR

This paper analyzes wave dispersion in pulsar plasma across different inertial frames, emphasizing Lorentz transformations, and reveals how wave modes transform between frames, including the emergence of additional modes.

## Contribution

It introduces a Lorentz-invariant formulation of wave dispersion in pulsar plasma and compares different relativistic distribution functions for the plasma.

## Key findings

- Lorentz transformation relates plasma dispersion functions in different frames.
- Wave modes can transform into additional modes under Lorentz boosts.
- Invariant dispersion equations imply a one-to-one correspondence of wave modes across frames.

## Abstract

Wave dispersion in a pulsar plasma is discussed emphasizing the relevance of different inertial frames, notably the plasma rest frame ${\cal K}$ and the pulsar frame ${\cal K}'$ in which the plasma is streaming with speed $\beta_{\rm s}$. The effect of a Lorentz transformation on both subluminal, $|z|<1$, and superluminal, $|z|>1$, waves is discussed. It is argued that the preferred choice for a relativistically streaming distribution should be a Lorentz-transformed J\"uttner distribution; such a distribution is compared with other choices including a relativistically streaming Gaussian distribution. A Lorentz transformation of the dielectric tensor is written down, and used to derive an explicit relation between the relativistic plasma dispersion functions in ${\cal K}$ and ${\cal K}'$. It is shown that the dispersion equation can be written in an invariant form, implying a one-to-one correspondence between wave modes in any two inertial frames. Although there are only three modes in the plasma rest frame, it is possible for backward-propagating or negative-frequency solutions in ${\cal K}$ to transform into additional forward-propagating, positive-frequency solutions in ${\cal K}'$ that may be regarded as additional modes.