Charging axially symmetric interior solutions in General Relativity

TL;DR

This paper introduces new solution-generating methods in General Relativity to construct charged and magnetized interior solutions with axial symmetry, expanding the set of exact solutions for anisotropic fluid sources.

Contribution

It develops generalized Ehlers-Harrison transformations for anisotropic fluids, enabling the derivation of new exact interior solutions with electric and magnetic fields in axial symmetry.

Findings

Derived charged and magnetized Zipoy-Vorhees interior solutions.

Presented solutions for electrically charged Bowers and Liang model.

Analyzed properties of the new exact solutions.

Abstract

We present two solution-generating techniques, which are direct generalizations of certain Ehlers-Harrison transformations in the Ernst formalism, while adapted to work in presence of an anisotropic fluid source with axial symmetry. Based on these procedures, we were able to construct the electrically charged and the magnetized solution for any static axially-symmetric geometry, which is sourced in general by an anisotropic fluid described by a non-diagonal anisotropic stress-energy tensor. As our main examples we derived and analyzed two new exact solutions with axial symmetry that describe the electrically charged Zipoy-Vorhees interior solution as well as the magnetized Zipoy-Vorhees interior solution, and presented some of their properties. As further examples of our solution-generating techniques we show how to derive two new solutions describing the electrically charged version of the Bowers and Liang solution, as well as a magnetized version of an exact solution with axial symmetry.