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It is shown that the extremal Reissner-Nordstr\"{o}m black hole, thenon-extremal one with multiple scattering particles, and the Schwarzschildblack hole with radial head-on particles are stable under the collision of theparticles near the horizon, if the back-reaction effect and the effectgenerated by gravity of particles are involved. Moreover, the collision nearReissner-Nordstr\"{o}m black holes with astrophysically typical mass can notgenerate the Planck-scale center-of-mass energy. However, the head-on collisionnear the typical primordial black hole could just occur at the Planck-energyscale.

Can the Reissner-Nordstr\"{o}m black hole or Schwarzschild black hole be the stable Planck-scale particle accelerator?