Classification of the non-null electrovacuum solution of Einstein-Maxwell equations with three-parameter abelian group of motions

TL;DR

This paper classifies all electrovacuum Stackel spaces with a three-parameter abelian symmetry group, providing explicit solutions for zero and non-zero cosmological constants, thus completing the classification of these spaces.

Contribution

It provides a complete classification of electrovacuum Stackel spaces with three-parameter abelian symmetry, including explicit solutions for different cosmological constant cases.

Findings

Complete list of electrovacuum Stackel spaces constructed.

Explicit solutions for zero cosmological constant using elementary functions.

Solutions with non-zero cosmological constant involve nonlinear differential equations.

Abstract

The classification of the Stackel spaces of the electrovacuum of the type (3.0) has been done. These spaces are invariant under the action of the three-parameter abelian group of motions and belong to the first type Bianchi spaces. In the case of a non-zero cosmological term, the metrics and potentials contain solutions of a nonlinear ordinary differential equation of the second order. When the cosmological term equals zero, the metrics and the components of the electromagnetic field tensor are expressed through elementary functions. Thus the classification of the electrovacuum Stackel spaces of all types is completed and complete list of these spaces is constructed.