Self-gravitating string-like configurations of nonlinear spinor fields (Q702848)

The authors discuss static, cylindrically symmetric configurations of a spinor field whose Lagrangian contains a nonlinearity of the arbitrary type F(S). They integrate the field equations in a general form and try to single out soliton-like solutions, having a) a regular axis of symmetry and b) such a geometry far from the axis that is seen by a distant observer as an isolated cylindrically symmetric matter distribution or a cosmic string. The authors review in the third chapter a previous paper [Gravit. Cosmol. 7, No. 3(27), 231--240 (2001; Zbl 1001.83054)], in which 4 non-existence theorems were formulated for static, cylindrically symmetric black holes, wormholes and hornlike solutions with regular asymptote. In the fourth chapter the authors consider the self gravitating spinor field, as follows 1) the integrations of the fields equations and 2) regularity of the solutions and example of a solitonic solution. After the calculation of the total electric charge the authors apply the regularity conditions to their solution. If the nonlinearity is taken as a power function with any real exponent, or as a polynomial, a solitonic solution cannot be produced. The difference between the spinor field behavior on a flat background and a self-gravitating spinor field consists in the fact, that the power law nonlinearities do not lead to finite energy and total charge of cylindrically symmetric field distributions in flat space but do so in the case of self-gravity. So, gravity plays a regularizing role, the authors conclude. An explicit example is given.