Light propagation in a plasma on Kerr spacetime. II. Plasma imprint on photon orbits

TL;DR

This paper investigates how a non-magnetized plasma affects light trajectories around Kerr black holes, revealing new phenomena such as multiple spherical orbits and off-equatorial circular orbits, with implications for black hole imaging.

Contribution

It extends previous work by analyzing plasma effects on photon orbits in Kerr spacetime, introducing new orbit types and a formula for light deflection applicable inside and outside the ergoregion.

Findings

Existence of two different spherical light rays at the same point in the ergoregion with plasma.

Circular orbits can occur off the equatorial plane in Kerr spacetime with plasma.

Derived a new exact formula for light deflection angle in plasma environments.

Abstract

In this paper, light propagation in a pressure-free non-magnetized plasma on Kerr spacetime is considered, which is a continuation of our previous study [Phys. Rev. D 95, 104003 (2017)]. It is assumed throughout that the plasma density is of the form that allows for the separability of the Hamilton-Jacobi equation for light rays, i.e., for the existence of a Carter constant. Here we focus on the analysis of different types of orbits and find several peculiar phenomena which do not exist in the vacuum case. We start with studying spherical orbits and conical orbits. In particular, it is revealed that in the ergoregion in the presence of a plasma there can exist two different spherical light rays propagating through the same point. Then we study circular orbits and demonstrate that, contrary to the vacuum case, circular orbits can exist off the equatorial plane in the domain of outer communication of a Kerr black hole. Necessary and sufficient conditions for that are formulated. We also find a compact equation for circular orbits in the equatorial plane of the Kerr metric, with several examples developed. Considering the light deflection in the equatorial plane, we derive a new exact formula for the deflection angle which has the advantage of being directly applicable to light rays both inside and outside of the ergoregion. Remarkably, the possibility of a non-monotonic behavior of the deflection angle as a function of the impact parameter is demonstrated in the presence of a non-homogeneous plasma. Furthermore, in order to separate the effects of the black-hole spin from the effects of the plasma, we investigate weak deflection gravitational lensing. We also add some further comments to our discussion of the black-hole shadow which was the main topic of our previous paper.