Centrifugal acceleration of protons by a supermassive black hole

We have considered the centrifugal acceleration of charged particles in the magnetospheres of rotating massive black holes. The maximum values of Lorentz factors of accelerated particles are found by numerical and analytical methods. The maximum energies depend on the parameter of the magnetization of particles κ , which is the ratio of the frequency of rotation of the magnetic field lines of the magnetic field in the magnetosphere ΩF, to the nonrelativistic cyclotron frequency ωc, κ = ωc / ΩF >>1, and from the parameter α of the ratio of the toroidal magnetic field BT to the poloidal one BP, α = BT / BP. It is shown that for small toroidal fields, α < κ - 1/4, the maximum Lorentz factor γm is only the square root of the magnetization, γm = κ - 1/2, while for large toroidal fields, α > κ - 1/4, the maximum energy increases significantly, γm = κ - 2/3. However, the maximum possible acceleration, γm = κ - 1, is not achieved in the magnetosphere. We also estimate the maximum energies of protons accelerated in some galactic nuclei.