Spherical orbits around a Kerr black hole

A special class of orbits known to exist around a Kerr black hole are spherical -- with constant coordinate radii that not necessarily confined the equatorial plane. Spherical time-like were first studied by Wilkins almost 50 years ago. In present paper, we perform systematic and thorough study these orbits, encompassing extending previous works on them. We simplified forms for parameters orbits. The parameter space is then analysed in detail; particular, delineate boundaries between stable unstable bound unbound prograde retrograde Finally, provide analytic solutions geodesic equations, illustrate few representative examples