TITLE:
Spherical and Circular Non-Equatorial Photon Orbits around Kerr Black Holes
AUTHORS:
Leo Morgovsky
KEYWORDS:
Black Holes, Kerr Metric, Photon Trajectories, Null Geodesics, Orbits Instability
JOURNAL NAME:
Journal of High Energy Physics, Gravitation and Cosmology,
Vol.9 No.3,
July
27,
2023
ABSTRACT: By analytically solving the equation of azimuthal null geodesics for spherical photon trajectories, a parametric representation of the corresponding segment of the orbit is obtained. The solution parameter is the latitude coordinate. The dependences of the orbital radius on the black hole spinning parameter and the angle of inclination of its plane with respect to the rotation axis are calculated for flat circular non-equatorial orbits. It is proved that all spherical photon trajectories in the Kerr spacetime are unstable, as well as equatorial ones, and the critical photon orbits in the Schwarzschild metric.