Solitons of Induced Scalar Field and Their Stability

TL;DR

This paper derives exact soliton-like solutions for scalar and electromagnetic fields in cosmological models, identifying conditions for their stability and introducing special solutions like droplets and bags.

Contribution

It presents new exact solutions for scalar-electromagnetic systems in cosmological backgrounds, analyzing their stability and introducing novel droplet, anti-droplet, and bag configurations.

Findings

Stable solutions exist in FRW space-time with various interaction terms.

In G"odel universe, only droplet-like and hat-like solutions are stable under certain conditions.

Special solutions such as droplets, anti-droplets, and bags are constructed and analyzed.

Abstract

Exact particle-like static, spherically and/or cylindrically symmetric solutions to the equations of interacting scalar and electromagnetic field system have been obtained. We considered Freedman-Robertson-Walker (FRW) space-time as an external homogenous and isotropic gravitational field whereas the homogeneous and anisotropic Universe is given by the G$\ddot o$del model. Beside the usual solitonian solutions some special regular solutions know as droplets, anti-droplets and bags (confined in finite interval and having trivial value beyond it) have been obtained. 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 and the hat-like configurations may be stable, if they are located in the region where $g^{00}>0$.