Cylindrically symmetric solitons with nonlinear self-gravitating scalar fields

Summary: "Static, cylindrically symmetric solutions to nonlinear scalar-Einstein equations are considered. Regularity conditions on the symmetry axis and flat or string asymptotic conditions are formulated in order to select soliton-like solutions. Some nonexistence theorems are proved, in particular, theorems asserting (i) the absence of black-hole and wormhole-like cylindrically symmetric solutions for any static scalar fields minimally coupled to gravity, and (ii) the absence of solutions with a regular axis for scalar fields with the Lagrangian L=F(I), I=phi^alphaphi_alpha, for any function F(I) possessing a correct weak field limit. Exact solutions for scalar fields with an arbitrary potential function V(phi) are obtained by quadratures and are expressed in a parametric form in a few ways, where the parameter may be either the coordinate x, the phi field itself, or one of the metric coefficients. It is shown that soliton-like solutions exist only with V(phi) having a variable sign. Some explicit examples of the solutions (including a soliton-like one) and their flat-space limit are discussed."