the radial velocity along the poles, provides for a well collimated jet along the poles. From eq.(44) we see that one has only to ask for a background state where matter is concentrated on the plane of the disk with relatively empty poles, e.g. $g(\theta) \rightarrow 0$ for $\theta \rightarrow 0$ and $\theta \rightarrow \pi$, in order to obtain extremely large ejection velocities along the poles. The axial symmetry condition imposed on eq.(34) guarantees both axial symmetry and symmetry above and below the plane of the disk for the full solution. We see also that if one takes higher orders for $m$, the index of the Legendre polynomial solution to eq.(33), one obtains increasingly more critical angles at positions intermediary between $0$ and $\pi/2$ at which the angular velocity goes to zero. In fact, more complex geometries and asymmetric jets appear, as inferred observationally by e.g. Ferreira et al. (2006), if $m$ is taken as an arbitrary real number. However, modelling a situation where a polar jet dominates the ejection identifies $m=2$ as the leading order.

Notice that the qualitative behaviour of the solution is guaranteed by the exactness of the angular solution, the approximation $r<2GM/c^{2}$ used for solving the 