New Infinite Series of Einstein Metrics on Sphere Bundles from AdS Black Holes

TL;DR

This paper constructs an infinite series of explicit Einstein metrics on certain sphere bundles, derived from limits of AdS Kerr black holes, extending known homogeneous metrics to inhomogeneous higher-dimensional cases.

Contribution

It introduces a new method to generate infinite inhomogeneous Einstein metrics on sphere bundles from AdS black hole limits, generalizing previous homogeneous solutions.

Findings

Infinite series of Einstein metrics on S^2 x S^3 and S^3-bundles over S^2.

Reduction to known homogeneous metrics in special cases.

Extension to higher dimensions using AdS Kerr black holes.

Abstract

A new infinite series of Einstein metrics is constructed explicitly on S^2 x S^3, and the non-trivial S^3-bundle over S^2, containing infinite numbers of inhomogeneous ones. They appear as a certain limit of a nearly extreme 5-dimensional AdS Kerr black hole. In the special case, the metrics reduce to the homogeneous Einstein metrics studied by Wang and Ziller. We also construct an inhomogeneous Einstein metric on the non-trivial S^{d-2}-bundle over S^2 from a d-dimensional AdS Kerr black hole. Our construction is a higher dimensional version of the method of Page, which gave an inhomogeneous Einstein metric on CP^2\sharp\bar{CP^2}.