Are black holes totally black?

Geodesic completeness needs that near the horizon of a black hole there exist “white hole” geodesics, coming from the region inside the horizon. We give a classification of all such geodesics with energies E/m ≤ 1 for the Schwarzschild and Kerr black holes. Collisions of particles moving along the “white hole” geodesics with those moving along “black hole” geodesics are considered. Formulas for the increase in the energy of collision in the centre of mass frame are obtained, and the possibility of observation of high energy particles arriving from a black hole on the Earth is discussed.