Selected spherical photon orbits around a deformed Kerr black hole

TL;DR

This paper analyzes spherical photon orbits around a deformed Kerr black hole, revealing unique behaviors absent in circular orbits and differing from the standard Kerr case, through analytical calculations and illustrative examples.

Contribution

It introduces the study of spherical photon orbits in a deformed Kerr black hole, highlighting differences from the Kerr case and providing analytical and visual insights.

Findings

Spherical photon orbits are absent in circular orbits.

Analytical expressions for azimuthal change and node dragging are derived.

Illustrative examples demonstrate unique orbit behaviors.

Abstract

In this paper, we investigate so-called spherical photon orbits around a deformed Kerr black hole with an extra deformation parameter. The change in the azimuth $\Delta\varphi$ and the angle of dragging of nodes per revolution $\Delta\Omega $ of a complete latitudinal oscillated orbit is calculated analytically. Finally, representative six examples orbits are plotted out to illustrate how spherical photon orbits look like and exhibit some interesting behavior. Especially, this spherical photon orbits are absent in circular orbits and different from the Kerr case.