Exact Solutions to Einstein-Maxwell theory on Eguchi-Hanson Space

TL;DR

This paper presents explicit exact solutions to higher-dimensional Einstein-Maxwell theory with Eguchi-Hanson space, extending to non-stationary cases with cosmological constant, revealing asymptotically de-Sitter expanding regions.

Contribution

It provides the first explicit analytical solutions incorporating Eguchi-Hanson space in higher-dimensional Einstein-Maxwell theory, including non-stationary extensions with cosmological constant.

Findings

Solutions are explicitly constructed using known analytical functions.

Solutions can be extended to non-stationary cases with cosmological constant.

The solutions describe asymptotically expanding de-Sitter patches.

Abstract

In this article, we construct explicit analytical exact solutions to the six and higher dimensional Einstein-Maxwell theory. In all solutions, a subspace of the metric is the Eguchi-Hanson space where the metric functions are completely determined in terms of known analytical functions. Moreover, we find the solutions can be extended to non-stationary exact solutions to Einstein-Maxwell theory with cosmological constant. We show that the solutions are asymptotically expanding patches of de-Sitter spacetime.