Droplets in General Relativity: Exact Self-Consistent Solutions to the Interacting Scalar and Electromagnetic Field Equations

TL;DR

This paper presents exact, self-consistent solutions in general relativity for scalar, electromagnetic, and gravitational fields that form droplet-like configurations with zero mass and charge, highlighting differences between spherical and cylindrical symmetries.

Contribution

It introduces new exact solutions for scalar-electromagnetic-gravitational systems with specific symmetry properties and analyzes their physical characteristics and transformation possibilities.

Findings

Solutions have zero mass and charge outside the critical region.

Spherical droplet solutions can transform into soliton-like configurations.

Cylindrical droplet solutions cannot transform into solitons.

Abstract

It is shown, for the self-consistent system of scalar, electro-magnetic and gravitational fields in general relativity, that the equations of motion admit a special kind of solutions with spherical or cylindrical symmetry. For these solutions, the physical fields vanish and the space-time is flat outside of the critical sphere or cylinder. Therefore, the mass and the electric charge of these configurations are zero. The principal difference between droplet-like solutions with spherical symmetry and those with cylindrical one has been established. In the first case there exists a possibility of continuous transformation of droplet-like configuration into the solitonian one, when for the second case there is no such a possibility.