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Explore the intricacies of extreme black holes and their event horizons in this 46-minute lecture by Eric Woolgar at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the concept of quasi-Einstein equations and their solutions, focusing on static near horizon geometries of extreme black holes. Examine a rigidity theorem for quasi-Einstein metrics on closed manifolds with closed 1-forms, understanding the implications for positive, zero, and negative quasi-Einstein constants. Learn about the recent corrections and improvements to the characterization of the negative case, contributed by Eric Bahuaud, Sharmila Gunasekaran, Hari K Kunduri, and Will Wylie. Gain insights into advanced topics in spacetime geometry and mathematical physics as part of the Workshop on "Non-regular Spacetime Geometry" held at ESI in March 2023.
