Solutions to the Einstein-Maxwell-Current System with Sasakian maifolds

TL;DR

This paper constructs stationary solutions to the Einstein-Maxwell-current system using Sasakian manifolds, linking magnetic fields, electric currents, and space curvature through the contact form and an arbitrary inhomogeneity function.

Contribution

It introduces a novel method of generating solutions on Sasakian manifolds, connecting geometric structures with physical electromagnetic and current configurations.

Findings

Solutions incorporate arbitrary inhomogeneity functions.

Magnetic field and electric current are determined by the contact form.

Space curvature is influenced by the inhomogeneity function.

Abstract

We construct stationary solutions to the Einstein-Maxwell-current system by using the Sasakian manifold for the three-dimensional space. Both the magnetic field and the electric current in the solution are specified by the contact form of the Sasakian manifold. The solutions contain an arbitrary function that describes inhomogeneity of the number density of the charged particles, and the function determines the curvature of the space.