Mathematics Colloquia and Seminars

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I will review a series of results regarding the extremal limit of generic black holes. We will see that in AdS, at low temperatures there are large tidal forces at the horizon. These tidal forces lead to weak null singularity in the extremal limit. Asymptotically flat black holes in the Einstein-Maxwell theory in four dimensions are free of these pathologies. However, they reappear after the addition of higher-derivative corrections. Thus, one can see that the geometry of (nearly-)extremal black holes is surprisingly sensitive to UV physics.

TBA