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v3.2.2
abstract: Einstein's theory of general relativity admits solutions which describe black holes, regions of spacetime where the gravitational field is strong enough that light cannot escape. Observations indicate that black holes are common in the universe, and interactions of black holes provide an important source for gravitational radiation. The Kerr family of rotating black holes provides the only viable model these phenomena, and it is therefore of fundamental importance to prove that the Kerr solution to the Einstein equations is unique and stable. In this talk I will discuss some of the remarkable geometric properties of the Kerr black holes, which are expected to be important in proving the uniqueness and stability of the Kerr black hole.