Stationary Einstein-Maxwell fields in arbitrary dimensions

TL;DR

This paper investigates higher-dimensional Einstein-Maxwell equations with multiple symmetries, formulates them as harmonic maps, and presents new exact solutions including rotating black holes and black rings in arbitrary dimensions.

Contribution

It generalizes the Ernst system to higher dimensions and provides new exact solutions like rotating black holes and black rings with electromagnetic fields.

Findings

Existence of electric, magnetic, and twist potentials proved.

Formulation as harmonic map on three-dimensional base space.

New solutions include electromagnetic Myers-Perry and static charged black rings.

Abstract

The Einstein-Maxwell equations in D-dimensions admitting (D-3) commuting Killing vector fields have been investigated. The existence of the electric, magnetic and twist potentials have been proved. The system is formulated as the harmonic map coupled to gravity on three-dimensional base space generalizing the Ernst system in the four-dimensional stationary Einstein-Maxwell theory. Some classes of the new exact solutions have been provided, which include the electro-magnetic generalization of the Myers-Perry solution, which describes the rotating black hole immersed in a magnetic universe, and the static charged black ring solution.