New asymptotically flat Einstein--Maxwell instantons

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.