Cylindrically Symmetric Solitons with Nonlinear Self-Gravitating Scalar Fields
arXiv:gr-qc/0101086
Abstract
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 non-existence 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 , , for any function possessing a correct weak field limit. Exact solutions for scalar fields with an arbitrary potential function are obtained by quadratures and are expressed in a parametric form in a few ways, where the parameter may be either the coordinate , or the field, or one of the metric coefficients. Soliton-like solutions are shown to exist only with having a variable sign. Some explicit examples of solutions (including a soliton-like one) and their flat-space limit are discussed.}
13 pages, Latex-2e