Title: Near Horizon Geometries and Quasi-Einstein metrics
Abstract: Extremal black holes in general relativity admit a
well-defined Near Horizon Geometry that describes the geometry of the
space time near its event horizon. Einstein's equations on the
Lorentzian space time imply that that the Riemannian metric on Near
Horizon Geometry satisfies an equation involving the Ricci curvature
and a smooth vector field X called the Quasi Einstein equation.
Comparison geometry and rigidity phenomena on Quasi Einstein metrics
have been previously studied in Riemannian geometry. In this talk I'll
discuss adaptations of work on Quasi Einstein Riemannian geometry that
give obstructions and rigidity for near horizon geometries, as well as
interesting examples of Quasi Einstein metrics coming from the near
horizon literature.