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

TL;DR

This paper investigates the stability of Reissner-Nordström and Schwarzschild black holes as potential Planck-scale particle accelerators, considering back-reaction effects and particle gravity, and finds conditions under which Planck-energy collisions are possible.

Contribution

It demonstrates that certain black holes can be stable particle accelerators at the Planck scale when accounting for back-reaction and gravitational effects of particles.

Findings

Reissner-Nordström black holes can be stable under particle collisions near the horizon.

Typical astrophysical black holes cannot produce Planck-scale energies through collisions.

Primordial black holes can facilitate Planck-energy head-on collisions.

Abstract

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.