Spherical null geodesics of rotating Kerr black holes

Abstract

The non-equatorial spherical null geodesics of rotating Kerr black holes are studied analytically. Unlike the extensively studied equatorial circular orbits whose radii are known analytically, no closed-form formula exists in the literature for the radii of generic (non-equatorial) spherical geodesics. We provide here an approximate formula for the radii r_{ph}(a/M;cos i) of these spherical null geodesics, where a/M is the dimensionless angular-momentum of the black hole and cos i is an effective inclination angle (with respect to the black-hole equatorial plane) of the orbit. It is well-known that the equatorial circular geodesics of the Kerr spacetime (the prograde and the retrograde orbits with cos i=\pm 1) are characterized by a monotonic dependence of their radii r_{ph}(a/M;cos i=\pm 1) on the dimensionless spin-parameter a/M of the black hole. We use here our novel analytical formula to reveal that this well-known property of the equatorial circular geodesics is actually not a generic property of the Kerr spacetime. In particular, we find that counter-rotating spherical null orbits in the range (3\sqrt{3}-\sqrt{59})/4 \lesssim \cos i<0 are characterized by a non-monotonic dependence of r_{ph}(a/M;cos i=const) on the dimensionless rotation parameter a/M of the black hole. Furthermore, it is shown that spherical photon orbits of rapidly-rotating black holes are characterized by a critical inclination angle, cos i=\sqrt{4/7}, above which the coordinate radii of the orbits approach the black-hole radius in the extremal limit. We prove that this critical inclination angle signals a transition in the physical properties of the spherical null geodesics: in particular, it separates orbits which are characterized by finite proper distances to the black-hole horizon from orbits which are characterized by infinite proper distances to the horizon.

13 pages

References in corpus (8)

• Slow relaxation of rapidly rotating black holes
• Universal Bound on Dynamical Relaxation Times and Black-Hole Quasinormal Ringing
• The Quasinormal Mode Spectrum of a Kerr Black Hole in the Eikonal Limit
• Hairy Black Holes and Null Circular Geodesics
• Unstable circular null geodesics of static spherically symmetric black holes, Regge poles and quasinormal frequencies
• The fastest way to circle a black hole
• Near-Extreme Black Holes and the Universal Relaxation Bound
• Resonance and absorption spectra of the Schwarzschild black hole for massive scalar perturbations: a complex angular momentum analysis

Cited by in corpus (41)

• Calculating black hole shadows: Review of analytical studies
• Understanding photon sphere and black hole shadow in dynamically evolving spacetimes
• Upper bound on the radii of black-hole photonspheres
• Periodic orbits around a spherically symmetric naked singularity
• Transient Instability of Rapidly Rotating Black Holes
• Silhouettes of invisible black holes
• Stable photon orbits in stationary axisymmetric electrovacuum spacetimes
• Lux in obscuro: Photon Orbits of Extremal Black Holes Revisited
• Exact Formulas for Spherical Photon Orbits Around Kerr Black Holes
• General Approach on Shadow Radius and Photon Spheres in Asymptotically Flat Spacetimes and the Impact of Mass-Dependent Variations
• The extreme orbital period in scalar hairy kerr black holes
• Lower bound on the radii of black-hole photonspheres
• Universal bounds on the size of a black hole
• Analyzing the Influence of Geometrical Deformation on Photon Sphere and Shadow Radius: A New Analytical Approach -- Spherically Symmetric Spacetimes
• Spherical photon orbits around a rotating black hole with quintessence and cloud of strings
• Analytic study of self-gravitating polytropic spheres with light rings
• Observability of spherical photon orbits in near-extremal Kerr black holes
• Lux in obscuro II: Photon Orbits of Extremal AdS Black Holes Revisited
• Near-horizon geodesics of high-spin black holes
• Self-gravitating ring of matter in orbit around a black hole: The innermost stable circular orbit
• Upper bound on the gravitational masses of stable spatially regular charged compact objects
• Extremal black holes have external light rings
• The existence of null circular geodesics outside extremal spherically symmetric asymptotically flat hairy black holes
• Constant-$r$ geodesics in the Painleve-Gullstrand form of Lense-Thirring spacetime
• Upper bound on the radii of regular ultra-compact star photonspheres
• Radii of spherical photon orbits around Kerr-Newman black holes
• Photon Boomerang in a Nearly Extreme Kerr Metric
• Electrogeodesics in the di-hole Majumdar-Papapetrou spacetime
• Upper bounds on the compactness at the innermost light ring of anisotropic horizonless spheres
• Black Holes in Lorentz-Violating Gravity: Thermodynamics, Geometry, and Particle Dynamics
• Strong-field gravitational lensing by black holes
• Spherical timelike orbits around Kerr black holes
• Analyzing the Influence of Geometrical Deformation on Photon Sphere and Shadow Radius: A New Analytical Approach -Stationary, and Axisymmetric Spacetime
• No short hair behaviors of ultra-compact stars
• Generic spherically symmetric thin-shell wormholes with equilibrium throat at the innermost photonsphere are unstable
• Gravitational Black Hole Shadow Spectroscopy
• Mass and spin coevolution of black holes inspiralling through dark matter
• Marginally bound circular orbits in the composed black-hole-ring system
• Relativistic Motion of Stars Near Rotating Black Hole
• Visible shapes of black holes M87* and SgrA*
• Images and photon regions of continuous photon sphere spacetime