We investigate the geometry near the horizon of a generic, four-dimensional
extremal black hole. When the cosmological constant is negative, we show that
(in almost all cases) tidal forces diverge as one crosses the horizon, and this
singularity is stronger for larger black holes. Nevertheless, all scalar
curvature invariants remain finite. Moreover, we show that nonextremal black
holes have tidal forces that diverge in the extremal limit. Holographically,
this singularity is reflected in anomalous scaling of the specific heat with
temperature. Similar (albeit weaker) effects are present when the cosmological
constant is positive, but not when it vanishes.
