Photon motion in Kerr-de Sitter spacetimes

Abstract

We study general non-equatorial motion of photons in the Kerr-de Sitter black hole and naked singularity spacetimes. The motion is governed by the impact parameter $X$ related to axial symmetry of the spacetime, and impact parameter $q$ related to its hidden symmetry. Appropriate 'effective potentials' governing the latitudinal and radial motion are introduced and their behaviour is examined by 'Chinese boxes' technique giving regions allowed for the motion in terms of the impact parameters. Limits on the impact parameter $X$ and $q$ are established in dependence on the spacetime parameters $M,\Lambda ,a$. The motion can be of orbital type (crossing the equatorial plane, $q>0$) and vortical type (tied above or bellow 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 motion in the radial direction, which, e. g., exclude possibility of existence of vortical motion of constant radius. Several other consequences are determined and a classification of Kerr-de Sitter spacetimes reflecting the behaviour of the effective potentials is given.

33 pages,84 figures

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Cited by in corpus (14)

• Light escape cones in local reference frames of Kerr-de Sitter black hole spacetimes and related black hole shadows
• Test particle motion around black hole in Einstein-Maxwell-scalar theory
• Investigating effects of dark matter on photon orbits and black hole shadows
• Black hole shadow to probe modified gravity
• Estimating the cosmological constant from shadows of Kerr--de Sitter black holes
• Spherical photon orbits in the field of Kerr naked singularities
• Profiled spectral lines of Keplerian rings orbiting in the regular Bardeen black hole spacetimes
• Integrability of Kerr-Newman spacetime with cloud strings, quintessence and electromagnetic field
• Maximal Kerr de Sitter spacetimes
• General Relativistic Aberration Equation and Measurable Angle of Light Ray in Kerr--de Sitter Spacetime
• Third type of spacetime with the coexistence of integrability and non-integrability
• Evolution of Braneworld Kerr-Newman Naked Singularities
• Possible influence of a cosmic repulsion on large-scale jets: geometric viewpoint
• Shadows of naked singularities and superspinars related to the revisited Kerr-de Sitter spacetimes