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Rigidity of the extremal Kerr-Newman horizon

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TWT - Twistor theory

The Einstein equations for a spacetime containing an extremal horizon induce a set of equations determined completely by quantities intrinsic to a compact cross-section of the horizon. Significant progress on classifying solutions to these equations was recently made by Dunajski and Lucietti, who showed that any non-static vacuum solution must admit a Killing vector field.   I will present joint work with David Katona and James Lucietti extending the Dunajski-Lucietti proof to four-dimensional Einstein-Maxwell theory. It follows that any non-trivial cross-section in this theory is given by the extremal Kerr-Newman family. I will also discuss the wider class of quasi-Einstein equations and rule out non-trivial solutions on compact surfaces of non-zero genus.

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

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