Description of Charged Scalar System by means of General Relativit y Approach

TL;DR

This paper uses a Kähler metric to find an exact solution to Einstein's equations with a charged scalar field's energy-momentum tensor, determining the scalar field function within a general relativistic framework.

Contribution

It introduces a novel exact solution of Einstein equations incorporating a charged scalar field using a Kähler metric approach.

Findings

Derived an exact Einstein solution with charged scalar field

Determined the scalar field function explicitly

Demonstrated the applicability of Kähler metrics in this context

Abstract

The K\"ahler metric which has been constructed by present author is used in this paper to find an exact solution of Einstein equations with energy-momentum tensor of special type. The type of $T_{ij}$ admits in particular to use it as energy-momentum tensor of charged scalar field and in case of such system the field function is determined.