Bernardo Hipolito Fernandes: Introduction to ALF metrics - a visual survey

Abstract

ALF metrics are a particular case of gravitational instantons, i.e. solutions of the vacuum Einstein equations. The Riemannian-Schwarzschild metric and the Taub-NUT metric are two examples of such solutions.
The aim of this talk is to understand what ALF metrics are and if something can be said about its rigidity. In order to achieve this, we will travel through different ideas in Riemannian Geometry.
We will not try to focus on the details but more on the geometric interpretation of the different concepts. No prior knowledge in Riemannian Geometry is required.