Spinor fields in spherically symmetric space-time

.Within the scope of a spherically symmetric space-time we study the role of a nonlinear spinor field in the formation of different configurations with spherical symmetries. The presence of the non-diagonal components of energy-momentum tensor of the spinor field leads to some severe restrictions on the spinor field itself. Since the spinor field is the source of the gravitational one, the metric function also changes in accordance with it. The system as a whole possesses solutions only in the case of some additional conditions on metric functions.