New class of exact solutions to Einstein-Maxwell-dilaton theory on four-dimensional Bianchi type IX geometry

TL;DR

This paper introduces new cosmological solutions to five-dimensional Einstein-Maxwell-dilaton theory based on four-dimensional Bianchi type IX geometry, covering various coupling constants and cosmological constant values, including special Eguchi-Hanson cases.

Contribution

It presents novel classes of non-stationary, conformally regular solutions with detailed analysis of different coupling constants and special geometries like Eguchi-Hanson type II.

Findings

Solutions are non-stationary and conformally regular.

Includes cases with positive, negative, and zero cosmological constant.

Extends to special geometries like Eguchi-Hanson type II.

Abstract

We construct new classes of cosmological solution to the five dimensional Einstein-Maxwell-dilaton theory, that are non-stationary and almost conformally regular everywhere. The base geometry for the solutions is the four-dimensional Bianchi type IX geometry. In the theory, the dilaton field is coupled to the electromagnetic field and the cosmological constant term, with two different coupling constants. We consider all possible solutions with different values of the coupling constants, where the cosmological constant takes any positive, negative or zero values. In the ansatzes for the metric, dilaton and electromagnetic fields, we consider dependence on time and two spatial directions. We also consider a special case of the Bianchi type IX geometry, in which the geometry reduces to that of Eguchi-Hanson type II geometry and find a more general solution to the theory.