Gravitational Instantons and special geometry

TL;DR

This paper investigates the Chen-Teo gravitational instanton, revealing it is Hermitian but not Kähler, and concludes all known gravitational instantons share these properties, challenging classical black hole uniqueness assumptions.

Contribution

It demonstrates that the Chen-Teo instanton is Hermitian and non-Kähler, establishing a new property of known gravitational instantons and providing insights into their geometric structure.

Findings

Chen-Teo instanton is Hermitian

Chen-Teo instanton is non-Kähler

All known gravitational instantons are Hermitian

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.