Kerr Black hole shadows in Melvin magnetic field with stable photon orbits

TL;DR

This paper investigates the shadows of Kerr black holes immersed in Melvin magnetic fields, revealing the existence of stable and unstable photon orbits, their dependence on magnetic field strength, and resulting distinctive shadow structures.

Contribution

It introduces the analysis of stable photon orbits in Melvin-Kerr black holes and their influence on shadow morphology, a novel aspect not previously explored.

Findings

Stable photon orbits exist alongside unstable ones in Melvin-Kerr spacetime.

Black hole shadows exhibit gray regions indicating stable photon orbits.

Shadow structures transition from panoramic to half-panoramic as magnetic field strength varies.

Abstract

We have studied the spacetime of a Kerr black hole immersed in Melvin magnetic field, and found not only unstable light rings could exist, but also stable light rings could exist. Both the prograde and retrograde unstable light rings radiuses increase with the magnetic field parameter $B$, but it is the opposite for stable light rings. The existence of unstable, stable light rings depend on both the rotation parameter $a$ and the magnetic field parameter $B$. For a certain $a$, there are both the prograde and retroprade unstable (stable) light rings when $B$ is less than a critical value $B_{c}$ of retrograde light ring. In this case, the shadows of Melvin-Kerr black hole have two gray regions on both sides of the middle main shadow, which correspond to the prograde and retrograde stable photon orbits. The photons in stable orbits are always moving around Melvin-Kerr black hole, they can't enter the black hole or escape to infinity. As $B$ continues to increase, there is only the prograde unstable (stable) light ring. In this case, the gray region only emerges in the life of the main shadow, which corresponds to the prograde stable photon orbits. The absence of the retrograde unstable (stable) light rings makes the Melvin-Kerr black hole shadow an half-panoramic (equatorial) shadow. When $B$ is bigger than $B_{C}$ of prograde light ring, neither prograde nor retroprade unstable (stable) light rings exist. In this case, the shadow of Melvin-Kerr black hole has no gray region for stable photon orbits, and becomes a panoramic (equatorial) shadow. In addition, there also exist some self-similar fractal structures in the shadow of Melvin-Kerr black hole arising from the chaotic motion of photon.