Can Quantum Particles Cross a Horizon?

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.