Abstract
We consider the problem of the existence of soliton-like self-gravitating cylindrically symmetric configurations of a classical spinor field with the nonlinearity F(S) (\(S = \bar \psi \psi \), F is an arbitrary function). Soliton-like configurations should have, by definition, a regular axis of symmetry and a flat or string-like geometry far from the axis (i.e., an asymptotically Minkowskian metric with a possible angular defect). It is shown that these conditions can be fulfilled if F(S) is finite as S → ∞ and decreases faster than S 2 as S → 0. The set of field equations is entirely integrated, and some explicit examples are considered. A regularizing role of gravity is discussed.
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Bronnikov, K.A., Chudayeva, E.N. & Shikin, G.N. Self-Gravitating String-Like Configurations of Nonlinear Spinor Fields. General Relativity and Gravitation 36, 1537–1545 (2004). https://doi.org/10.1023/B:GERG.0000032146.03936.45
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DOI: https://doi.org/10.1023/B:GERG.0000032146.03936.45