radial problem will only introduce an error in the actual values of the radial velocities outside of $r<2GM/c^{2}$, but will not change the fact that velocities will be of radial infall along the plane of the disk, $\theta=\pi/2$, and of radial outflow along the poles (where the background solution becomes very small), the jet solution for $\theta=0,\pi$.

The two constants of the problem, $\bar{\rho}_{0}$ and $\bar{\rho}_{J}$, can now be calculated once a choice of $g(\theta)$ is specified, from the two conditions:

$$\dot{M}_{a} =2\pi \int_{0}^{\pi} \rho_{0}V_{0} sin(\theta) r^{2} d\theta,$$

$$\dot{M}_{j} =2\pi \int_{0}^{\theta_{J}} \rho_{1}V_{1} sin(\theta) r^{2} d\theta,$$

where $\theta_{J}$ is a suitable angle defining the opening of the jet, in all likelihood very small, as will be see in the following section. In the above equations $\dot{M}_{a}$ gives the matter accretion rate onto the central star, and $\dot{M}_{j}$ the matter ejection rate due to the jet. Dimensionally, the two quantities above will scale as:

$$\dot{M}_{a} =C_{a}  \frac{ \left( \pi G   M \right)^{2}  }{c^{3}} \bar{\rho}_{0}$$

$$\dot{M}_{j} =C_{j}  \frac{ \left( \pi G   M \right)^{2}  }{c^{3}} \frac{\bar{\rho}_{J}^{2}}{\bar{\rho}_{0}},$$

where $C_{a}$ and $C_{j}$ are two dimensionless constants which will depend on the choice of $g_{\theta}$, and which would be expected to be of order 1.

Qualitatively, this 