Light propagation in a plasma on an axially symmetric and stationary spacetime: Separability of the Hamilton-Jacobi equation and shadow

TL;DR

This paper investigates how light propagates around compact objects in a plasma within a stationary, axisymmetric spacetime, deriving conditions for analytical solutions of photon paths and shadows in various astrophysical models.

Contribution

It formulates conditions for separability of the Hamilton-Jacobi equation in plasma-filled spacetimes, enabling analytical calculation of photon regions and shadows for complex metrics.

Findings

Derived conditions for Hamilton-Jacobi separability in plasma environments.

Analytical determination of photon regions and shadows in multiple spacetime models.

Demonstrated applicability to Kerr black holes, wormholes, and other astrophysical objects.

Abstract

The properties of light rays around compact objects surrounded by a plasma are affected by both strong gravitational fields described by a general-relativistic spacetime and by a dispersive and refractive medium, characterized by the density distribution of the plasma. We study these effects employing the relativistic Hamiltonian formalism under the assumption of stationarity and axisymmetry. The necessary and sufficient conditions on the metric and on the plasma frequency are formulated, such that the rays can be analytically determined from a fully separated Hamilton-Jacobi equation. We demonstrate how these results allow to analytically calculate the photon region and the shadow, if they exist. Several specific examples are discussed in detail: the "hairy" Kerr black holes, the Hartle-Thorne spacetime metrics, the Melvin universe, and the Teo rotating traversable wormhole. In all of these cases a plasma medium is present as well.