5-Dimensional Covariance and Generation of Solutions of Einstein Equations

TL;DR

This paper presents a method leveraging 5-dimensional covariance in Kaluza-Klein theory to generate exact 4-dimensional Einstein solutions with electromagnetic and scalar fields from vacuum solutions, linking physical and geometric properties.

Contribution

It introduces a novel generation procedure based on 5D covariance that produces Einstein solutions with additional fields from vacuum solutions using coordinate transformations.

Findings

Derived relations between physical properties and geometric invariants.

Established a systematic method for solution generation in Einstein equations.

Connected 5D covariance with 4D physical fields.

Abstract

A generation procedure, based on the 5-dimensional covariance of the Kaluza-Klein theory, is developed. The procedure allows one to obtain exact solutions of the 4-dimensional Einstein equations with electromagnetic and scalar fields from vacuum 5-dimensional solutions using special 5-dimensional coordinate transformations. Relations between the physical properties of the resulting solutions and invariant geometrical properties of the generating Killing vectors are found out.