Can the Reissner-Nordstr\"{o}m black hole or Schwarzschild black hole be   the stable Planck-scale particle accelerator?
  It is shown that the extremal Reissner-Nordstr\"{o}m black hole, the non-extremal one with multiple scattering particles, and the Schwarzschild black hole with radial head-on particles are stable under the collision of the particles near the horizon, if the back-reaction effect and the effect generated by gravity of particles are involved. Moreover, the collision near Reissner-Nordstr\"{o}m black holes with astrophysically typical mass can not generate the Planck-scale center-of-mass energy. However, the head-on collision near the typical primordial black hole could just occur at the Planck-energy scale. 
Yi Zhu, Shao-Feng Wu, Yin Jiang and Guo-Hong Yang
hep-th astro-ph.HE gr-qc