Abstract

We present a review of the Penrose process and its modifications in relation to the Kerr black holes and naked singularities (superspinars). We introduce the standard variant of this process, its magnetic version connected with magnetized Kerr black holes or naked singularities, the electric variant related to electrically charged Schwarzschild black holes, and the radiative Penrose process connected with charged particles radiating in the ergosphere of magnetized Kerr black holes or naked singularities. We discuss the astrophysical implications of the variants of the Penrose process, concentrating attention to the extreme regime of the magnetic Penrose process leading to extremely large acceleration of charged particles up to ultra-high energy E∼1022 eV around magnetized supermassive black holes with mass M∼1010M⊙ and magnetic intensity B∼104 G. Similarly high energies can be obtained by the electric Penrose process. The extraordinary case is represented by the radiative Penrose process that can occur only around magnetized Kerr spacetimes but just inside their ergosphere, in contrast to the magnetic Penrose process that can occur in a more extended effective ergosphere determined by the intensity of the electromagnetic interaction. The explanation is simple, as the radiative Penrose process is closely related to radiated photons with negative energy whose existence is limited just to the ergosphere.

Highlights

  • The Penrose process [1] introduces the extraction of rotational energy from rotating black holes, or their counterparts represented by naked singularities, by using the decay of particles in the ergosphere, a region of extremely strong influence of the spacetime rotation, allowing for the existence of particles with negative energy relative to distant observers

  • We consider magnetized Kerr black holes and discuss the two regimes of the magnetic Penrose process and its applicability to the creation of ultra-high energy protons observed in cosmic rays; note that in the magnetic Penrose process the back-reaction effect due to radiation of the charge particles moving in the external magnetic field plays an important role [30,31]

  • If the decay of charged particles is considered, it was shown that the magnetic Penrose process (MPP) around magnetized rotating black holes, i.e., Kerr black holes immersed in an external, large-scale magnetic fields, can have a much larger efficiency than the pure Penrose process, exceeding the annihilation value of η = 1 [42,43]

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Summary

Introduction

The Penrose process [1] introduces the extraction of rotational (or electrostatic) energy from rotating (charged) black holes, or their counterparts represented by naked singularities (or superspinars), by using the decay of particles in the ergosphere, a region of extremely strong influence of the spacetime rotation, allowing for the existence of particles with negative energy relative to distant observers. We consider magnetized Kerr black holes (or naked singularities) and discuss the two regimes of the magnetic Penrose process and its applicability to the creation of ultra-high energy protons observed in cosmic rays; note that in the magnetic Penrose process the back-reaction effect due to radiation of the charge particles moving in the external magnetic field plays an important role [30,31]. We introduce the notion of a radiative Penrose process as a fundamentally new version that can be related to the radiative self-reaction that occurs solely in the ergosphere; it can be realized only around magnetized Kerr black holes, the effective ergosphere of the radiating particle is irrelevant in this case.

Kerr Black Holes and the Penrose Process
Kerr Geometry and Ergosphere
Test Particle Motion and Locally Non-Rotating Frames
The Penrose Process
Magnetized Kerr Black Holes and Magnetic Penrose Process
The Role of Magnetic Fields in Black Hole Physics
Asymptotically Uniform Magnetic Field as Basic Approximation
Hamiltonian Formalism and Effective Potential of the Motion
Chaotic Scattering
Magnetic Penrose Process and Creation of Jets
Moderately Efficient Regime of Mpp
Extremely Efficient Regime of Mpp
Ultra-High Energy Cosmic Rays as Products of Mpp in the Extreme Regime
Synchrotron Radiation of Accelerated Charged Particles
Electric Penrose Process
Energy of Ionized Particles
Radiative Penrose Process
Landau–Lifshitz Equations of Motion under Radiative Force
Conclusions
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