Bianchi IX geometry and the Einstein-Maxwell theory

TL;DR

This paper constructs and analyzes numerical and exact solutions in higher-dimensional Einstein-Maxwell theory using Bianchi IX geometry, revealing near-regular solutions that interpolate between known geometries and exploring their cosmological implications.

Contribution

It introduces a method to generate higher-dimensional Einstein-Maxwell solutions based on Bianchi IX geometry, including numerical superpositions and exact cosmological solutions.

Findings

Solutions are almost regular except at a singular point.

Solutions interpolate between Eguchi-Hanson type I and II geometries.

Constructed exact cosmological solutions with specific properties.

Abstract

We construct numerical solutions to the higher-dimensional Einstein-Maxwell theory. The solutions are based on embedding the four dimensional Bianchi type IX space in the theory. We find the solutions as superposition of two functions, which one of them can be found numerically. We show that the solutions in any dimensions, are almost regular everywhere, except a singular point. We find that the solutions interpolate between the two exact analytical solutions to the higher dimensional Einstein-Maxwell theory, which are based on Eguchi-Hanson type I and II geometries. Moreover, we construct the exact cosmological solutions to the theory, and study the properties of the solutions.