Scalar Field with Induced Nonlinearity: Regular Solutions and their Stability

TL;DR

This paper derives exact static, spherically and cylindrically symmetric solutions for scalar and electromagnetic fields in general relativity, analyzing their stability in different cosmological models.

Contribution

It presents new exact solutions for scalar-electromagnetic systems in GR and examines their stability in FRW and G"odel universe models.

Findings

Stable solutions exist in FRW space-time for various interactions.

G"odel model solutions are only stable as droplet-like configurations in certain regions.

Solutions depend on the type of interaction term considered.

Abstract

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 $g^{00}>0$.