Seminarium Teorii Względności i Grawitacji

We argue that an extremal limit ($T\to0$) of a generic black hole in AdS$_4$ has a singular horizon. That leaves imprints on black hole thermodynamics. Moreover, an infalling observer would notice large tidal forces, even at finite temperatures. Similar, albeit weaker, observations also hold for a positive cosmological constant but not when it vanishes. However, this fine-tuning is removed by quantum effects. Thus, even quantum-corrected extremal Kerr is singular, at least for the matter content of the standard model. This result should remain valid for any approach to quantum gravity.