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Intrinsic rigidity of extremal horizons and black hole uniqueness

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TWT - Twistor theory

I will present a recent proof which shows that the intrinsic geometry of compact cross-sections of any vacuum extremal horizon, possibly with a cosmological constant, must admit a Killing vector field. In particular, this implies that the extremal Kerr horizon is the most general such horizon in four-dimensional General Relativity and completes the classification of the associated near-horizon geometries.  I will also discuss a recent uniqueness proof which shows that any analytic Einstein spacetime with positive cosmological constant, that contains a static extremal horizon with a maximally symmetric compact cross-section, is the extremal Schwarzschild de Sitter spacetime or its near-horizon geometry.

This talk is part of the Isaac Newton Institute Seminar Series series.

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