Characterisation of circular light rays in a plasma

TL;DR

This paper characterizes circular light rays in an unmagnetised plasma within axially symmetric, stationary spacetimes, introducing potentials to analyze their properties and extending topological methods from vacuum to plasma cases.

Contribution

It introduces a novel potential-based framework to analyze circular light rays in plasma, generalizing existing methods from vacuum spacetimes.

Findings

Potentials identify circular light rays in plasma.

Plasma influences centrifugal force on light rays.

Examples provided for Minkowski, Schwarzschild, Kerr, and NUT spacetimes.

Abstract

It is the purpose of this paper to give a characterisation of circular light rays in a plasma on an axially symmetric and stationary spacetime. We restrict to the case of an unmagnetised, pressure-free electron-ion plasma and we assume that the plasma shares the symmetry of the spacetime. As a main tool we use two potentials, one for prograde and one for retrograde light rays, whose critical points are exactly the circular light rays in the plasma. In the case that the plasma density vanishes, the corresponding equipotential surfaces reduce to the relativistic Von Zeipel cylinders which have been discussed in many papers since the 1970s. In a plasma, the gradients of the potentials give the centrifugal and the Coriolis forces experienced by a light ray, where the plasma has an influence only on the centrifugal force. The introduction of these potentials allows us to generalise topological methods that have been successfully used for proving the existence or non-existence of circular vacuum light rays to the plasma case. The general results are illustrated with examples on Minkowski, Schwarzschild, Kerr and NUT spacetimes.