  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. In particular, this applies to
generic nonspherical black holes, such as those satisfying inhomogeneous
boundary conditions. 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.
