Study of Ultra-High-Energy Cosmic Rays Based on the Monopole

Ultra-high-energy cosmic rays are charged particles with energies greater than1\,\mathrmEeV that come from outer space. In this paper, we mainly discuss a supermassive black hole model with magnetic monopoles as a potential source of ultra-high-energy cosmic rays, with particle acceleration driven by electric fields. Firstly, based on the constraints of magnetic charge within black hole spacetime, we show that particles can be accelerated to energies on the order of 10⁸ EeV in both general and extremal black hole scenarios, with no restrictions on the type of magnetic charge. Next, with the assumption of Newtonian-saturated magnetic monopole abundance, we find that supermassive black hole with electroweak monopole cannot accelerate particles to ultra-high-energy. Then, considering the black hole accretion effects, we find that the particle maximum energy can be accelerated from 1 EeV to 10⁴ EeV for typical black holes with massesM = 10⁶−10¹⁰ \mathrmM_\odot. Finally, we discuss the nonlinear electrodynamics coupled to the general relativity model as a possible source of ultra-high-energy cosmic rays, where the energy of accelerated particles can reach values on the order 10⁸ EeV.