Fubini-Study geometries in the higher-dimensional gravity

TL;DR

This paper constructs approximate higher-dimensional Einstein-Maxwell solutions based on Fubini-Study geometries, revealing their uniqueness and limitations in including a cosmological constant.

Contribution

It introduces a method to generate approximate solutions using Fubini-Study Kahler manifolds and analyzes their properties and uniqueness in higher dimensions.

Findings

Solutions are expressible as integrals of special functions.

Solutions are regular except at a bolt point.

Solutions cannot be extended to include a cosmological constant.

Abstract

We construct approximate solutions to the Einstein-Maxwell theory with uplifting the four dimensional Fubini-Study Kahler manifold. We find the solutions can be expressed as the integrals of two special functions. The solutions are regular almost everywhere except a bolt structure on a single point in any dimensionality. We also show that in the context of considered ansatzes for the metric function and the Maxwell field, the solutions are unique and can not be non-trivially extended to include the cosmological constant in any dimensions.