**Publication date:** Nov 2018

**Abstract:**

For the Kerr naked singularity (KNS) spacetimes, we study properties of

spherical photon orbits (SPOs) confined to constant Boyer-Lindquist

radius r. Some new features of the SPOs are found, having no

counterparts in the Kerr black hole (KBH) spacetimes, especially stable

orbits that could be pure prograde/retrograde, or with turning point in

the azimuthal direction. At r>1 (r<1) the covariant photon energy

E> 0 (E< 0), at r=1 there is E= 0. All unstable orbits must have

E> 0. It is shown that the polar SPOs can exist only in the

spacetimes with dimensionless spin a < 1.7996. Existence of closed

SPOs with vanishing total change of the azimuth is demonstrated.

Classification of the KNS and KBH spacetimes in dependence on their

dimensionless spin a is proposed, considering the properties of the

SPOs. For selected types of the KNS spacetimes, typical SPOs are

constructed, including the closed paths. It is shown that the stable

SPOs intersect the equatorial plane in a region of stable circular

orbits of test particles, depending on the spin a. Relevance of this

intersection for the Keplerian accretion discs is outlined and

observational effects are estimated.

**Authors:**

Charbulák, Daniel; Stuchlík, Zdeněk;