Fubini–Study geometries in the higher-dimensional gravity

Abstract

We construct approximate solutions to the Einstein–Maxwell theory with uplifting the four-dimensional Fubini–Study Kähler 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 cannot be nontrivially extended to include the cosmological constant in any dimensions.