Analytical study of light ray trajectories in Kerr spacetime in the presence of an inhomogeneous anisotropic plasma

TL;DR

This paper derives exact analytical solutions for light ray trajectories around Kerr black holes in the presence of an inhomogeneous, anisotropic plasma, using Hamilton-Jacobi methods and elliptic integrals.

Contribution

It introduces a novel analytical approach to model light propagation in Kerr spacetime with complex plasma structures, expanding understanding of photon paths in such environments.

Findings

Exact solutions for light trajectories in Kerr spacetime with plasma

Analytical expressions using elliptic integrals and Mino time

Three-dimensional visualizations of photon paths

Abstract

We calculate the exact solutions to the equations of motion that govern the light ray trajectories as they travel in a Kerr black hole's exterior that is considered to be filled with an inhomogeneous and anisotropic plasmic medium. This is approached by characterizing the plasma through conceiving a radial and an angular structure function, which are let to be constant. The description of the motion is carried out by using the Hamilton-Jacobi method, that allows defining two effective potentials, characterizing the evolution of the polar coordinates. The elliptic integrals of motion are then solved analytically, and the evolution of coordinates is expressed in terms of the Mino time. This way, the three-dimensional demonstrations of the light ray trajectories are given respectively.