Conformastatic disk-haloes in Einstein-Maxwell gravity

TL;DR

This paper develops a relativistic model of a thin disk with a surrounding halo in Einstein-Maxwell gravity, providing explicit solutions that are asymptotically flat, singularity-free, and satisfy energy conditions.

Contribution

It introduces a new conformastatic spacetime model with electromagnetic fields, solving Einstein-Maxwell equations using harmonic functions for the first time in this context.

Findings

The model is asymptotically flat and free of singularities.

The solutions satisfy all energy conditions.

Electromagnetic and gravitational potentials are determined by harmonic functions.

Abstract

We present a relativistic model describing a thin disk surrounded by a halo in presence of an electromagnetic field. The model is obtained by solving the Einstein-Maxwell equations on a particular conformastatic spacetime background and by using the distributional approach for the energy-momentum tensor. A class of solutions is obtained in which the gravitational and electromagnetic potentials are completely determined by a harmonic function only. A particular solution is given that is asymptotically flat and singularity-free, and satisfies all the energy conditions.