Stationary Axisymmetric Solutions of the Einstein Equations with Rigidly Rotating Perfect Fluid and Nonlinear Charged Sources

TL;DR

This paper presents an exact solution to Einstein's equations describing a stationary, rigidly rotating perfect fluid coupled with nonlinear electromagnetic fields, expanding understanding of such complex astrophysical systems.

Contribution

It introduces a new exact solution for Einstein equations with nonlinear electromagnetic sources, specifically for the Carter B(+) branch with a specific equation of state.

Findings

Solution is of Petrov type D.

Electromagnetic eigenvectors align with Debever-Penrose vectors.

Uses a duality-invariant Born-Infeld nonlinear electrodynamics.

Abstract

A class of stationary rigidly rotating perfect fluid coupled with non-linear electromagnetic fields was investigated. An exact solution of the Einstein equations with sources for the Carter B(+) branch was found, for the equation of state $3p + \epsilon = constant$. We use a structural function for the Born-Infeld non-linear electrodynamics which is invariant under duality rotations and a metric possessing a four- parameter group of motions. The solution is of Petrov type D and the eigenvectors of the electromagnetic field are aligned to the Debever-Penrose vectors.