  We consider generic static spacetimes with Killing horizons and study
properties of curvature tensors in the horizon limit. It is determined that the
Weyl, Ricci, Riemann and Einstein tensors are algebraically special and
mutually aligned on the horizon. It is also pointed out that results obtained
in the tetrad adjusted to a static observer in general differ from those
obtained in a free-falling frame. This is connected to the fact that a static
observer becomes null on the horizon.
  It is also shown that finiteness of the Kretschmann scalar on the horizon is
compatible with the divergence of the Weyl component $\Psi_{3}$ or $\Psi_{4}$
in the freely falling frame. Furthermore finiteness of $\Psi_{4}$ is compatible
with divergence of curvature invariants constructed from second derivatives of
the 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 objects
the structure of the Einstein tensor on the horizon changes due to extra terms
as compared to the usual horizons, the null energy condition being violated at
some portions of the horizon surface. The demand to rule out such divergencies
leads to the constancy of the factor that governs the leading term in the
asymptotics of the lapse function and in this sense represents a formal analog
of the zeroth law of mechanics of non-extremal black holes. In doing so, all
extra terms in the Einstein tensor automatically vanish.
