Extremal black holes are special solutions of Einstein’s equations with maximal spin or charge for their mass. In this minicourse, I will describe (and report on progress resolving) a series of conjectures explaining the role of extremal black holes in gravitational collapse and their relation to the threshold of black hole formation and critical phenomena. The material will be based on joint work with Yannis Angelopoulos (BIMSA) and Christoph Kehle (MIT).

In this first lecture, I will give an introduction to extremal black holes, their geometry, and the main conjectures: the third law of black hole thermodynamics, the extremal critical collapse conjecture, and the extremal event horizon threshold conjecture. I will then give an overview of what we know about these conjectures so far.