We present a review of the influence of cosmic repulsion and external magnetic fields on accretion disks rotating around rotating black holes and on jets associated with these rotating configurations. We consider both geometrically thin and thick disks. We show that the vacuum energy represented by the relic cosmological constant strongly limits extension of the accretion disks that is for supermassive black holes comparable to extension of largest galaxies, and supports collimation of jets at large distances from the black hole. We further demonstrate that an external magnetic field crucially influences the fate of ionized Keplerian disks causing creation of winds and jets, enabling simultaneously acceleration of ultra-high energy particles with energy up to ${10}^{21}$ eV around supermassive black holes with $M\sim {10}^{10}{M}_{\odot }$ surrounded by sufficiently strong magnetic field with $B\sim {10}^4$ G. We also show that the external magnetic fields enable existence of “levitating” off-equatorial clouds or tori, along with the standard equatorial toroidal structures, if these carry a non-vanishing, appropriately distributed electric charge.

We study the motion of charged particles in the field of a rotating black hole immersed into an external asymptotically uniform magnetic field, focusing on the epicyclic quasicircular orbits near the equatorial plane. Separating the circular orbits into four qualitatively different classes according to the sign of the canonical angular momentum of the motion and the orientation of the Lorentz force, we analyze the circular orbits using the so-called force formalism. We find the analytical solutions for the radial profiles of velocity, specific angular momentum, and specific energy of the circular orbits in dependence on the black-hole dimensionless spin and the magnetic field strength. The innermost stable circular orbits are determined for all four classes of the circular orbits. The stable circular orbits with an outward-oriented Lorentz force can extend to radii lower than the radius of the corresponding photon circular geodesic. We calculate the frequencies of the harmonic oscillatory motion of the charged particles in the radial and vertical directions related to the equatorial circular orbits and study the radial profiles of the radial, ${\omega }_{\mathrm{r}}$; vertical, ${\omega }_{\theta }$; and orbital, ${\omega }_{\varphi }$, frequencies, finding significant differences in comparison to the epicyclic geodesic circular motion. The most important new phenomenon is the existence of toroidal charged particle epicyclic motion with ${\omega }_{\mathrm{r}}\sim {\omega }_{\theta }\gg {\omega }_{\varphi }$ that could occur around retrograde circular orbits with an outward-oriented Lorentz force. We demonstrate that for the rapidly rotating black holes the role of the “Wald induced charge” can be relevant.

The study of quasi-periodic oscillations (QPOs) of X-ray flux observed in the stellar-mass black hole binaries can provide a powerful tool for testing of the phenomena occurring in the strong gravity

The production and acceleration mechanisms of ultrahigh-energy cosmic rays (UHECRs) of energy >10²⁰ eV, clearly beyond the GZK cutoff limit, remain unclear, which points to the exotic nature of the phenomena. Recent observations of extragalactic neutrinos may indicate that the source of UHECRs is an extragalactic supermassive black hole (SMBH). We demonstrate that ultraefficient energy extraction from a rotating SMBH driven by the magnetic Penrose process (MPP) could indeed fit the bill. We envision ionization of neutral particles, such as neutron beta decay, skirting close to the black hole horizon that energizes protons to over 10²⁰ eV for an SMBH of mass 10⁹ M _⊙ and magnetic field 10⁴ G. Applied to the Galactic center SMBH, we have a proton energy of order ≈10^15.6 eV that coincides with the knee of the cosmic-ray spectra. We show that large γ _z factors of high-energy particles along the escaping directions occur only in the presence of an induced charge of the black hole, which is known as the Wald charge in the case of a uniform magnetic field. It is remarkable that the process requires neither an extended acceleration zone nor fine-tuning of accreting-matter parameters. Further, this leads to certain verifiable constraints on the SMBH’s mass and magnetic field strength as the source of UHECRs. This clearly makes the ultraefficient regime of the MPP one of the most promising mechanisms for fueling the UHECR powerhouse.

In this Letter, we wish to point out that the distinguishing feature of magnetic Penrose process (MPP) is its super high-efficiency exceeding |$100\hbox{ per cent}$| (which was established in mid 1980s for discrete particle accretion) of extraction of rotational energy of a rotating black hole electromagnetically for a magnetic field of milli Gauss order. Another similar process, which is also driven by the electromagnetic field, is Blandford–Znajek mechanism (BZ) that could be envisaged as high magnetic field limit MPP as it requires threshold magnetic field of order 10⁴ G. Recent simulation studies of fully relativistic magnetohydrodynamic (MHD) flows have borne out super high-efficiency signature of the process for high magnetic field regime; viz BZ. We would like to make a clear prediction that similar simulation studies of MHD flows for low magnetic field regime, where BZ would be inoperative, would also have superefficiency.

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∼${10}^{22}$ eV around magnetized supermassive black holes with mass M∼${10}^{10}$$M_{\odot }$ and magnetic intensity B∼${10}^4$ 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.