Gravitational Instantons, old and new

TL;DR

This paper reviews gravitational instantons, which are special solutions to Einstein equations in four dimensions that produce complete, non-compact metrics resembling flat space at infinity, highlighting various examples and their properties.

Contribution

It provides a comprehensive overview of both classical and recent gravitational instantons, emphasizing their geometric structures and significance in theoretical physics.

Findings

Catalogs known gravitational instantons and their properties

Highlights new examples and classifications of instantons

Discusses the role of instantons in quantum gravity

Abstract

This is a review of gravitational instantons -- solutions to Riemannian Einstein or Einstein-Maxwell equations in four dimensions which yield complete metrics on non-compact four-manifolds, and which asymptotically `look like' flat space. The review focuses on examples, and is based on lectures given by the author at the Cracow School of Theoretical Physics held in Zakopane in June 2024.