We consider only a special type of motion off the equatorial plane when particles are moving quasiradially along the trajectories on which the value of the polar angle θ remains constant, θ = θ₀. For this motion

 (1.1)

If we exclude trivial solutions θ₀ = 0, θ₀ = π, and θ₀ = π/2, the relations between the integrals of motion can be written in the form

 (1.2)

 (1.3)

Hence, motion with constant θ = θ₀ is possible only when Ẽ > 1 (infinite motion).

Non-relativistic particles moving at parabolic velocity (v_∞ = 0) and with zero angular momentum (l_z = 0) represent a special limiting case. Such particles fall at constant θ and are dragged into the rotation around the black hole.

Another important limiting case is the falling of ultrarelativistic particles (photons) which move at infinity at θ = constant. In this limit, Ẽ → ∞and l_z →∞ while their ratio b = l_z/Ẽ remains finite and equal to b = a sin2 θ. The null vector n^μ tangent to a null geodesic representing the motion of the in-coming photon is

 (1.4)

If one substitutes 1 instead of −1 into the right-hand side of this expression one obtains a congruence of outgoing photons. These two null congruences are known as the principal null congruences of the Kerr metric. They are geodesic and shear free. They satisfy the following relations:

 (1.5)

where C_{αβγ δ} is the Weyl tensor. Since the Kerr metric is a vacuum solution, the Weyl tensor is equal to the Riemann tensor. The principal null vectors in the Kerr geometry also obey the relation

 (1.6)

where F = -g_{t t} = 1 - 2Mr/Σ.