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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-K\"ahler. It follows that all known examples of gravitational instantons
are Hermitian.