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The study of charged particle dynamics in the combined gravitational and magnetic field can provide important theoretical insight into astrophysical processes around black holes. In this paper, we explore the charged particle dynamics in parabolic magnetic field configuration around Schwarzschild black hole, since the paraboloidal shapes of magnetic field lines around black holes are well motivated by the numerical simulations and supported by observations of relativistic jets. Analysing the stability of bounded orbits and using the effective potential approach, we show the possibility of existence of stable circular off-equatorial orbits around the symmetry axis. We also show the influence of radiation reaction force on the dynamics of charged particles, in particular on the chaoticity of the motion and Poincaré sections, oscillatory frequencies, and emitted electromagnetic spectrum. Applied to Keplerian accretion disks, we show that in parabolic magnetic field configuration, the thin accretion configurations can be either destroyed or transformed into a thick toroidal structure given the radiation reaction and electromagnetic-disk interactions included. Calculating the Fourier spectra for radiating charged particle trajectories, we find that the radiation reaction force does not affect the main frequency peaks, however, it lowers the higher harmonics making the spectrum more flat and diluted in high frequency range.

A non-monotonic behavior of the velocity gradient of a test particle revolving around a rapidly rotating black hole in the locally non-rotating frame of reference is known as the Aschenbach effect. This effect can serve as a distinguishing signature of rapidly rotating black holes, being potentially useful for the measurements of the astrophysical black hole spins. This paper is the generalization of our previous research to the motion of spinning particles around a rotating black hole with non-zero cosmological constant. We show that both the particle’s spin s and the cosmological constant Λ modify the critical value of the black hole spin ac, for which the Aschenbach effect can be observed; ac can increase or decrease depending on the signs of s and Λ. We also found that the particle’s spin s can mimic the effect of the cosmological constant Λ for a given ac, causing thus a discrepancy in the measurements of s, Λ and ac in the Aschenbach effect.

Buchdahl star is the most compact object without an event horizon and is an excellent candidate for a black hole mimicker. Unlike black holes, rotating Buchdahl star can be over-extremal with respect to the black hole, sustaining a larger spin. We show that it can also develop an ergosphere above the threshold spin β > 1 / 2 , which allows extraction of its rotational energy. Electromagnetic field around Buchdahl star is also expected to differ from that of black hole in both strength and topology. In this paper, we explore the energetics of Buchdahl star focusing on the magnetic Penrose process in the two magnetic field configurations, i.e., uniform and dipole. Below the threshold spin, Buchdahl star is expected to be quiet, while above the threshold it can be much more efficient than the black hole if a dipolar magnetic field is developed on its surface.

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 regime. Magnetized versions of the standard geodesic models of QPOs can explain the observationally fixed data from the three microquasars. We perform a successful fitting of the HF QPOs observed for three microquasars, GRS 1915+105, XTE 1550-564 and GRO 1655-40, containing black holes, for magnetized versions of both epicyclic resonance and relativistic precession models and discuss the corresponding constraints of parameters of the model, which are the mass and spin of the black hole and the parameter related to the external magnetic field. The estimated magnetic field intensity strongly depends on the type of objects giving the observed HF QPOs. It can be as small as 10 - 5  G if electron oscillatory motion is relevant, but it can be by many orders higher for protons or ions (0.02–1 G), or even higher for charged dust or such exotic objects as lighting balls, etc. On the other hand, if we know by any means the magnetic field intensity, our model implies strong limit on the character of the oscillating matter, namely its specific charge.

We investigate the dynamics of charged test particles in the vicinity of magnetized black hole mimickers, such as gravastars, wormholes, and ultracompact Buchdahl stars, modeled by a Schwarzschild spacetime with an external dipole magnetic field originating inside the mimicker. The interaction between gravity and electromagnetism is characterized by a single dimensionless “magnetic” parameter b that controls the relative strength and orientation of the Lorentz force. We provide a complete classification of equatorial and off-equatorial circular orbits across all regimes of the magnetic parameter, with particular emphasis on the strong-field region below the photon sphere. We show that stable off-equatorial circular orbits arise only under magnetic repulsion and originate at the radii where equatorial orbits become marginally unstable to vertical perturbations. Remarkably, such off-equatorial orbits can remain stable even inside the photon sphere, preventing direct particle infall as in geodesic motion. We further analyze epicyclic oscillations around stable orbits and discuss their relevance for high-frequency quasi-periodic oscillations observed in many black hole systems. Outside the regime of regular oscillations, we study chaotic charged particle motion in belts concentrated around off-equatorial circular orbits, including the effects of radiative back-reaction, which may be relevant to coronae around accretion disks. Finally, we study the ionization of initially Keplerian disks and demonstrate qualitatively different dynamical outcomes for magnetically repelled and attracted particles. We present possible observational signatures of the considered black hole mimickers, most notably the existence of a high-energy particle repulsive barrier located under the photon sphere.

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 ∼ 10 10 M ⊙ surrounded by sufficiently strong magnetic field with B ∼ 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.

Magnetic Penrose process (MPP) is not only the most exciting and fascinating process mining the rotational energy of black hole but it is also the favored astrophysically viable mechanism for high energy sources and phenomena. It operates in three regimes of efficiency, namely low, moderate and ultra, depending on the magnetization and charging of spinning black holes in astrophysical setting. In this paper, we revisit MPP with a comprehensive discussion of its physics in different regimes, and compare its operation with other competing mechanisms. We show that MPP could in principle foot the bill for powering engine of such phenomena as ultra-high-energy cosmic rays, relativistic jets, fast radio bursts, quasars, AGNs, etc. Further, it also leads to a number of important observable predictions. All this beautifully bears out the promise of a new vista of energy powerhouse heralded by Roger Penrose half a century ago through this process, and it has today risen in its magnetically empowered version of mid 1980s from a purely thought experiment of academic interest to a realistic powering mechanism for various high-energy astrophysical phenomena.

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.

The simplest approach to include a mass into the electromagnetic vector potential is to modify the Einstein–Maxwell action to the Einstein–Proca form. There are currently no exact analytical solutions for this scenario. However, by using perturbation theory, where both the Proca mass and the black hole charge are small parameters, it is possible to find an exact analytical solution. In this solution, the metric tensor remains unchanged, but the vector potential deviates from the Coulomb potential. In particular, even if the Proca mass is limited by the value m γ < 10 - 48 g , which is the current experimental upper limit for photon mass, it makes a significant contribution to the dynamical equations. In this paper, we study the motion of neutral and charged particles in the vicinity of a weakly Proca-charged black hole, and test the observational implications of the solution of the Einstein–Proca equations for gravitational bending, the black hole shadow, and the fit to the orbits of the Galactic center flares observed by the near-infrared GRAVITY instrument. We find that only extremely cold photons, which are likely scattered before reaching a distant observer, could reveal the non-zero photon mass effect through the black hole shadow. For the Galactic center flare analysis we obtained constraints on the dimensionless Proca parameter to μ ≤ 0.125 for the electric interaction parameter in the range - 1.1 < Q < 0.5 , which can be potentially tested by future GRAVITY flare astrometry. Since the Proca parameter is coupled to the black hole mass, the effect of the Proca charge becomes more pronounced for supermassive black holes compared to stellar-mass objects. Our perturbative treatment remains valid essentially up to the horizon, with divergences appearing only in the immediate near-horizon region, where a fully non-perturbative analysis would be required.

We study spherically symmetric magnetically charged generic black hole solutions of general relativity coupled to non-linear electrodynamics (NED). For characteristic values of the generic spacetime parameters we give the position of horizons in dependence on the charge parameter, demonstrating separation of the black hole and no-horizon solutions, and possibility of existence of solutions containing three horizons. We show that null, weak and strong energy conditions are violated when the outer horizon is approaching the center. We study effective potentials for photons and massive test particles and location of circular photon orbits (CPO) and innermost stable circular orbit (ISCO). We show that the unstable photon orbit can become stable, leading to the possibility of photon capture which affects on silhouette of the central object. The position of ISCO approaches the horizon with increasing charge parameter q and the energy at ISCO decreases with increasing charge parameter. We investigate this phenomenon and summarize for a variety of the generic spacetime parameters the upper estimate on the spin parameter of the Kerr black which can be mimicked by the generic charged black hole solutions.