Gravitational Instantons and special geometry

Abstract

The Chen-Teo gravitational instanton is an asymptotically flat, toric, Ricci flat family of metrics on $\mathbb{C}{\mathbb{P}}^2\setminus S^1$, that provides a counterexample to the classical Euclidean Black Hole Uniqueness conjecture. In this paper we show that the Chen-Teo instanton is Hermitian and non-Kähler. It follows that all known examples of gravitational instantons are Hermitian.

Revised version, corrected typos and added references

Cited by in corpus (1)

• On self-dual Yang-Mills fields on special complex surfaces