We study the axial collimation of the vortical geodesics in the held o
f a rotating black hole. This effect manifests itself when the energy
and angular momenta of the particles that move on those geodesics vary
slowly in dynamical time. In this paper we deduce the constraints tha
t ensure collimation and show how the latter arises when the orbital p
arameters are perturbed by a given electromagnetic field or by pressur
e gradients.