New asymptotically flat Einstein--Maxwell instantons

TL;DR

This work constructs a new three-parameter family of asymptotically flat Einstein-Maxwell instantons on $M=\mathbb{CP}^2\setminus S^1$, extending the Chen-Teo vacuum instantons and providing explicit counterexamples to the Euclidean Black Hole Uniqueness conjecture in the Einstein-Maxwell setting. It starts from a six-parameter ALF toric geometry and, through rod-structure regularity, produces AF solutions with zero NUT charge, including explicit mass $m$, angular momentum $j$, and Maxwell charges $(\mathcal{Q},\mathcal{P})$, while remaining conformally Kähler and of Weyl type $D$. These instantons illuminate the semi-classical structure of coupled gravitational and electromagnetic fields and, via a Kaluza-Klein lift, connect to five-dimensional supergravity. The results motivate a broader classification program for toric AF Einstein-Maxwell instantons and prompt further study of their twistor and integrable-systems descriptions.

Abstract

We disprove the Euclidean Einstein--Maxwell Black Hole Uniqueness Conjecture, and thus demonstrate that the semi-classical properties of coupled gravitational and electromagnetic fields are more subtle than expected from Lorentzian general relativity, where the Kerr-Newman family of metrics yields the most general stationary and asymptotically flat black holes with a single event horizon. This is achieved by an explicit construction of a new three--parameter family of asymptotically flat Einstein--Maxwell instantons. These solutions are toric, regular, and free of conical and orbifold singularities on the manifold $M=\CP^2\setminus S^1$. In the case of vanishing charge, these instantons reduce to the Chen--Teo Ricci flat instantons.