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 G$\ddot o$del 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 G$\ddot o$del model only the droplet-like configurations may be stable, if they are located in the region where $g^{00}>0$.