Maciej Dunajski (University of Cambridge) – Gravitational instantons, old and new

Gravitational instantons are Riemannian solutions to Einstein equations in four dimensions which yield complete metrics on non-compact four-manifolds, and which asymptotically `look like' flat space. Their study has been initiated by Stephen Hawking in his quest for Euclidean quantum gravity, and since then lot of effort has been put to make the term ‘look– like’ into a precise mathematical statement. While Euclidean quantum gravity does not any-more aspire to a status of a fundamental theory, the study of gravitational instantons has influenced both theoretical physics and pure mathematics. I will give an elementary introduction to the subject, and focus on the recent retirement  of the Riemannian  black-hole uniqueness conjecture:  It is now known that there exist asymptotically flat gravitational instantons which can not be obtained as analytic continuations of  black hole solutions to imaginary time.