Scalar Field with Induced Nonlinearity: Regular Solutions and their Stability

Exact particle-like static, spherically and/or cylindrically symmetric solutions to the equations of interacting scalar and electromagnetic field system have been obtained within the scope of general relativity. In particular, we considered Freedman-Robertson-Walker (FRW) space-time as an external homogenous and isotropic gravitational field whereas the inhomogenous and isotropic Universe is given by the Gödel model. The solutions obtained have been thoroughly studied for different types of interaction term. It has been shown that in FRW space-time equations with different interaction terms may have stable solutions while within the scope of Gödel model only the dropletlike configurations may be stable, if they are located in the region where g > 0.