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We consider generic static spacetimes with Killing horizons and studyproperties of curvature tensors in the horizon limit. It is determined that theWeyl, Ricci, Riemann and Einstein tensors are algebraically special andmutually aligned on the horizon. It is also pointed out that results obtainedin the tetrad adjusted to a static observer in general differ from thoseobtained in a free-falling frame. This is connected to the fact that a staticobserver becomes null on the horizon.  It is also shown that finiteness of the Kretschmann scalar on the horizon iscompatible with the divergence of the Weyl component $\Psi_{3}$ or $\Psi_{4}$in the freely falling frame. Furthermore finiteness of $\Psi_{4}$ is compatiblewith divergence of curvature invariants constructed from second derivatives ofthe Riemann tensor.  We call the objects with finite Krestschmann scalar but infinite $\Psi_{4}$``truly naked black holes''. In the (ultra)extremal versions of these objectsthe structure of the Einstein tensor on the horizon changes due to extra termsas compared to the usual horizons, the null energy condition being violated atsome portions of the horizon surface. The demand to rule out such divergenciesleads to the constancy of the factor that governs the leading term in theasymptotics of the lapse function and in this sense represents a formal analogof the zeroth law of mechanics of non-extremal black holes. In doing so, allextra terms in the Einstein tensor automatically vanish.Comment: 21 pages, To appear in Class. Quant. Gra

Curvature tensors on distorted Killing horizons and their algebraic classification