Publication date: Dec 2017
Abstract:
We study the general motion of photons in the Kerr-de Sitter black-hole
and naked singularity spacetimes. The motion is governed by the impact
parameters X, related to the axial symmetry of the spacetime, and q,
related to its hidden symmetry. Appropriate `effective potentials‘
governing the latitudinal and radial motion are introduced and their
behavior is examined by the `Chinese boxes‘ technique giving regions
allowed for the motion in terms of the impact parameters. Restrictions
on the impact parameters X and q are established in dependence on the
spacetime parameters M, Λ , a. The motion can be of orbital type
(crossing the equatorial plane, q>0) and vortical type (tied above or
below the equatorial plane, q<0). It is shown that for negative
values of q, the reality conditions imposed on the latitudinal motion
yield stronger constraints on the parameter X than that following from
the reality condition of the radial motion, excluding the existence of
vortical motion of constant radius. The properties of the spherical
photon orbits of the orbital type are determined and used along with the
properties of the effective potentials as criteria of classification of
the KdS spacetimes according to the properties of the motion of the
photon.
Authors:
Charbulák, Daniel; Stuchlík, Zdeněk;