Evaporation screening, scattering, and quantum tunnelling near the horizons of Schwarzschild and Reissner-Nordström black holes

For the radial motion of massive particles with large angular momenta in Schwarzschild geometry and that of massive charged particles with large angular momenta or energy in a particular range in Reissner-Nordström geometry, there exist classically forbidden regions on the outside of the respective event horizons which scatter certain infalling geodesics or screen some of the black holes' evaporation by reflecting the emitted particles back into the black holes. Quantum tunnelling across this forbidden regions is studied.