Spherical null geodesics of rotating Kerr black holes

Understand

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.