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The study of the quasi-periodic oscillations (QPOs) of X-ray flux observed in the stellar-mass black hole (BH) binaries can provide a powerful tool for testing the phenomena occurring in strong gravity regime. We thus present and apply to three known microquasars the model of epicyclic oscillations of Keplerian discs orbiting rotating BHs governed by the modified theory of gravity (MOG). We show that the standard geodesic models of QPOs can explain the observationally fixed data from the three microquasars, GRO 1655-40, XTE 1550-564, and GRS 1915+105. We perform a successful fitting of the high frequency (HF) QPOs observed in these microquasars, under assumption of MOG BHs, for epicyclic resonance and its variants, relativistic precession and its variants, tidal disruption, as well as warped disc models and discuss the corresponding constraints of parameters of the model, which are the mass and spin and parameter α of the BH.

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.

The study of the quasi-periodic oscillations (QPOs) of X-ray flux observed in the stellar-mass black hole (BH) binaries or quasars can provide a powerful tool for testing the phenomena occurring in strong gravity regime. We thus fit the data of QPOs observed in the well known microquasars as well as active galactic nuclei (AGNs) in the framework of the model of geodesic oscillations of Keplerian disks modified for the epicyclic oscillations of spinning test particles orbiting Kerr BHs. We show that the modified geodesic models of QPOs can explain the observational fixed data from the microquasars and AGNs but not for all sources. We perform a successful fitting of the high frequency QPOs models of epicyclic resonance and its variants, relativistic precession and its variants, tidal disruption, as well as warped disc models, and discuss the corresponding constraints of parameters of the model, which are the spin of the test particle, mass and rotation of the BH.

To test the role of large-scale magnetic fields in accretion processes, we study the dynamics of the charged test particles in the vicinity of a black hole immersed into an asymptotically uniform magnetic field. Using the Hamiltonian formalism of the charged particle dynamics, we examine chaotic scattering in the effective potential related to the black hole gravitational field combined with the uniform magnetic field. Energy interchange between the translational and oscillatory modes of the charged particle dynamics provides a mechanism for charged particle acceleration along the magnetic field lines. This energy transmutation is an attribute of the chaotic charged particle dynamics in the combined gravitational and magnetic fields only, the black hole rotation is not necessary for such charged particle acceleration. The chaotic scatter can cause a transition to the motion along the magnetic field lines with small radius of the Larmor motion or vanishing Larmor radius, when the speed of the particle translational motion is largest and it can be ultra-relativistic. We discuss the consequences of the model of ionization of test particles forming a neutral accretion disc, or heavy ions following off-equatorial circular orbits, and we explore the fate of heavy charged test particles after ionization where no kick of heavy ions is assumed and only the switch-on effect of the magnetic field is relevant. We demonstrate that acceleration and escape of the ionized particles can be efficient along the Kerr black hole symmetry axis parallel to the magnetic field lines. We show that a strong acceleration of the ionized particles to ultra-relativistic velocities is preferred in the direction close to the magnetic field lines. Therefore, the process of ionization of Keplerian discs around the Kerr black holes can serve as a model of relativistic jets.

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 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.

We are fitting dynamics of electrically neutral hot-spot orbiting around Sagittarius A* (Sgr A*) source in Galactic center, represented by various modifications of the standard Kerr black hole (BH), to the three flares observed by the GRAVITY instrument on May 27, July 22, July 28, 2018. We consider stationary, axisymmetric, and asymptotically flat spacetimes describing charged BHs in general relativity (GR) combined with nonlinear electrodynamics, or reflecting the influence of dark matter (DM), or in so called parameterized dirty Kerr spacetimes, and test them using the hot-spot data. We show that the orbital frequencies as well as positions of the hot-spots orbiting the considered BHs fit the observed positions and periods of the flare orbits, and give relevant constraints on the parameters of the considered BH spacetimes and the gravity or other theories behind such modified spacetimes.

We study behaviour of ionized region of a Keplerian disk orbiting a Schwarzschild black hole immersed in an asymptotically uniform magnetic field. In dependence on the magnetic parameter \\[ B\\], and inclination angle \\[ \\] of the disk plane with respect to the magnetic field direction, the charged particles of the ionized disk can enter three regimes: (1) regular oscillatory motion, (2) destruction due to capture by the magnetized black hole, (3) chaotic regime of the motion. In order to study transition between the regular and chaotic type of the charged particle motion, we generate time series of the solution of equations of motion under various conditions, and study them by non-linear (box counting, correlation dimension, Lyapunov exponent, recurrence analysis, machine learning) methods of chaos determination. We demonstrate that the machine learning method appears to be the most efficient in determining the chaotic region of the \\[ -r\\] space. We show that the chaotic character of the ionized particle motion increases with the inclination angle. For the inclination angles \\[ 0\\] whole the ionized internal part of the Keplerian disk is captured by the black hole.

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.

In this article, we explore the dynamics of accretion structures encircling spherically symmetric black holes, comparing three accretion disk models with distinct angular momentum profiles: (i) the geometrically thin Keplerian disk, (ii) the Fishbone–Moncrief torus; and (iii) the Polish Doughnut. Employing general relativistic magnetohydrodynamics simulations with the High Accuracy Relativistic Magnetohydrodynamics code, we investigate these three models, considering the magnetic field’s influence on the accretion disk angular momentum redistribution. We show that the magnetic field is a key factor in accretion disk structures, especially in regions with lower mass density. Our investigation verifies the well-established fact that the presence of a magnetic field significantly influences the accretion rate and its temporal variability.