  The prevalent opinion that infalling objects can freely cross a black hole
horizon is based on the assumptions that the horizon region is governed by
classical General Relativity and by specific singular coordinate
transformations it is possible to remove divergences in the geodesic equations.
However, the coordinate transformations usually used to demonstrate the
geodesic completeness are of class $C^0$, while the standard causality theory
requires that the metric tensor to be at least $C^1$. Introduction of
$C^0$-class functions leads to the appearance of the additional delta-like
sources in the Einstein equations and in the equations for quantum particles.
Therefore, to explore the horizon region, in addition to the classical geodesic
equations, one needs to use equation of quantum particles. Applying physical
boundary conditions at the Schwarzschild and Kerr event horizons, we show
existence of the exponentially decay/enhanced solutions (with the complex
phases) to the Klein-Gordon equation. This means that in semi-classical
approximation particles probably do not enter the black hole horizon, but are
absorbed/reflected by it. Then it follows that the minimal classical size of
any isolated body is its horizon radius, what potentially can solve main black
hole mysteries.
