This paper explores the dynamics of both neutral and charged particles orbiting near a rotating black hole in scalar–tensor–vector gravity. We study the conditions for the particle to escape at the innermost stable circular orbit. We investigate the stability of orbits through the effective potential and Lyapunov exponent in the presence of a magnetic field. The effective force acting on particle is also discussed. We also study the center of mass energy of particle collision near the horizon of this black hole. Finally, we compare our results with the particle motion around Schwarzschild, Kerr and Schwarzschild-MOG black holes. It is concluded that the external magnetic field, spin parameter and dimensionless parameter of the theory have strong effects on the particle dynamics in modified gravity.

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 $$\alpha $$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.

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.

In this article, we try to capture the influence of deviation from standard Kerr black hole (BH) spacetime on observed high-frequency quasi-periodic oscillations (QPOs) signal. We explore the dynamics of test particles in the field of rotating compact objects governed by the various modifications of the standard Kerr BH spacetime and apply the model of epicyclic oscillations of Keplerian discs to the observed microquasars and active galactic nuclei high-frequency QPOs data. We present a generalized formalism for fitting two well-known high-frequency QPO models: the epicyclic resonance model and the relativistic precession model. This is done assuming stationary, axisymmetric, and asymptotically flat spacetimes. Recently, we have used the same set of stationary, axisymmetric, and asymptotically flat spacetimes, and estimated the restrictions of spacetime parameters with the help of hot-spot data of three flares observed at Sgr A* by GRAVITY instrument (Misbah Shahzadi et al 2022 Eur. Phys. J. C 82 407). The aim of this work is not to test a particular theoretical model or to determine and constrain its parameters, but to map a set of well-astrophysically motivated deviations from classical Kerr BH spacetime and demonstrate which ones provide the best fit for high-frequency QPOs data and could be fruitful for future exploration.

In this paper, we explore the chaotic signatures of the geodesic dynamics for particles moving in the slowly rotating Hartle-Thorne spacetime; an approximate solution of vacuum Einstein field equations describing the exterior of a massive, deformed, and slowly rotating compact object. We employ a numerical study to examine the geodesics of prolate and oblate deformations for generic orbits and find the plateaus of the rotation curve, which are associated with the existence of Birkhoff islands in the Poincaré surface of the section, where the ratio of the radial and polar frequency of geodesics remains constant throughout the island. We investigate various phase-space structures, including hyperbolic points and chaotic regions in the neighborhood of resonant islands. Moreover, chaotic behavior is observed to be governed by the stickiness phenomenon, where chaotic orbits remain attached to stable ones for an extended duration before eventually diverging and are attracted toward the surface of the neutron star. The precision of the numerical integration used to simulate the particle’s trajectories plays a crucial role in the structure of the Poincaré surface of the section. We present a comparison of several efficient structure-preserving numerical schemes of order four applied to the considered nonintegrable dynamical system and we investigate which schemes possess the canonical property of the Hamiltonian flow. In particular, we compare the performance of the symplectic Runge-Kutta integrator with the G-symplectic general linear method. Among the class of nonsymplectic integrators, we employ the explicit Runge-Kutta method and an explicit general linear method with a standard projection technique to project the numerical solution onto the desired manifold. The projection scheme admits the integration without any drift from the desired manifold and is computationally cost effective. We are concerned with two crucial aspects; long-term behavior and CPU time consumption.