TITLE:
Equatorial Circular and Spherical Photon Orbits around Kerr-Type Black Holes in Expanding Universe
AUTHORS:
Leo Morgovsky
KEYWORDS:
Black Hole, Photon Orbit, Cosmological Constant, Null Geodesics
JOURNAL NAME:
Journal of High Energy Physics, Gravitation and Cosmology,
Vol.12 No.4,
September
28,
2026
ABSTRACT: This paper investigates the effects that may arise in null (light-like) geodesics in the vicinity of Kerr-type black holes. Exact solutions for circular equatorial and spherical photon orbits are obtained using the geodesic equations of the Kerr-de Sitter metric, which includes the cosmological constant lambda. By solving the radial equation simultaneously with its first derivative, expressions for the photon angular momentum and Carter constant are derived. Based on these results, an equation for equatorial circular photon orbits around Kerr black holes is obtained, generalizing the well-known Bardeen-Press-Teukolsky formula to the case of a nonzero cosmological constant. An equation describing spherical photon orbits is also derived and solved, extending the known result of E. Teo to include the influence of the cosmological constant. A comparison between expressions with and without the cosmological constant makes it possible to estimate its potential influence and determine the threshold above which these effects become significant.