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Gravitational Instantons and special geometry (2112.11863v2)
Published 22 Dec 2021 in gr-qc and math.DG
Abstract: The Chen-Teo gravitational instanton is an asymptotically flat, toric, Ricci flat family of metrics on $\mathbb{C}\mathbb{P}2\setminus S1$, 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.