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.

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