Two-dimensional relativistic stellar wind

The anisotropic structure of the relativistic stellar wind is investigated. Both relativistic fluid velocity and relativistic temperature are taken into account. General analysis is carried out in the curvilinear coordinates and the generalization of the 'dispersion equation' is obtained. The topological structure of the individual field lines is the same as in the spherically-symmetric case, except the fact that the magnetic field dependence on distance cannot be established a priori. The interaction between neighbouring field lines brings the dependence on the 'transverse' coordinate, numbering the field lines. This dependence leads to the establishing of a new constraint on the global flow topology. The two-dimensional wind structure is analyzed, with the constraint taken into account, in the large distances limit, using the asymptotic expansion into the r^-1 power series. In the lowest order approximation the constraint reduces to a new global constant of motion. This constant causes the splitting of the two solution families.