  A new way to implement the causality condition on the event horizon of black
holes is discovered. The metric of a black hole is shown to be a function of
the complex-valued gravitational radius r_g => r_g + i0. The relation between
this modification of the metric and the causality condition is established
using the analyticity of the S-matrix, which describes scattering of probing
particles on a back hole. The found property of the metric has strong
manifestations in scattering and related phenomena. One of them is the
unexpected effect of reflection of incoming particles on the event horizon,
which strongly reduces the absorption cross section.
