Nonstationary self-gravitating configurations of scalar and electromagnetic fields

TL;DR

This paper introduces a new method for constructing exact nonstationary solutions involving scalar and electromagnetic fields in general relativity, overcoming the typical static or stationary limitations.

Contribution

The authors develop an approach to find nonstationary, spherically symmetric solutions with scalar and electromagnetic fields coupled to gravity, including an exact solution with nontrivial space-time topology.

Findings

Constructed an exact nonstationary solution with nontrivial topology.

Proposed a method based on an invariant equation involving the scalar potential.

Extended the class of known solutions beyond static or stationary configurations.

Abstract

Mathematical modeling of gravitating configurations of physical fields is one of the priority directions of the modern theory of gravity. Most of the exact solutions constructed within the framework of the general relativity are static or stationary configurations. This is due to the objective complexity of solving the Einstein equations under the assumption of nonstationarity. We present an approach to constructing nonstationary configurations of a spherically symmetric nonlinear real scalar field and the electromagnetic field, which areassumed both to be minimally coupled to gravity. It is based on the isolation of one invariant equation written in terms of the characteristic function and scalar field potential. Using the proposed method, an exact nonstationary solution with a nontrivial topology of space-time will be constructed.