Geodesic dynamics is regular in the fields of isolated stationary black holes. However, due to the presence of unstable periodic orbits, it easily becomes chaotic under various perturbations. Here, we examine what amount of stochasticity is induced in Schwarzschild space–time by the presence of an additional source. Following astrophysical motivation, we specifically consider thin rings or discs lying symmetrically around the hole, and describe the total field in terms of exact static and axially symmetric solutions of Einstein's equations. The growth of chaos in time‐like geodesic motion is illustrated on Poincaré sections, on time series of position or velocity and their Fourier spectra, and on time evolution of the orbital ‘latitudinal action’. The results are discussed in terms of dependence on the mass and position of the ring/disc and on geodesic parameters (energy and angular momentum). In the Introduction, we also add an overview of the literature.

The close neighborhood of a supermassive black hole contains not only the accreting gas and dust but also stellar-sized objects, such as late-type and early-type stars and compact remnants that belong to the nuclear star cluster. When passing through the accretion flow, these objects perturb it by the direct action of stellar winds, as well as their magnetic and gravitational effects. By performing general-relativistic magnetohydrodynamic simulations, we investigate how the passages of a star can influence the supermassive black hole gaseous environment. We focus on the changes in the accretion rate and the emergence of blobs of plasma in the funnel of an accretion torus. We compare results from 2D and 3D numerical computations that have been started with comparable initial conditions. We find that a quasi-stationary inflow can be temporarily inhibited by a transiting star, and the plasmoids can be ejected along the magnetic field lines near the rotation axis. We observe the characteristic signatures of the perturbing motion in the power spectrum of the accretion variability, which provides an avenue for a multi-messenger detection of these transient events. Finally, we discuss the connection of our results to multiwavelength observations of galactic nuclei, with the emphasis on ten promising sources (Sgr A*, OJ 287, J0849+5108, RE J1034+396, 1ES 1927+65, ESO 253–G003, GSN 069, RX J1301.9+2747, eRO-QPE1, and eRO-QPE2).

The dynamical system studied in previous papers of this series, namely a bound time-like geodesic motion in the exact static and axially symmetric space-time of an (originally) Schwarzschild black hole surrounded by a thin disc or ring, is considered to test whether the often employed "pseudo-Newtonian" approach (resorting to Newtonian dynamics in gravitational potentials modified to mimic the black-hole field) can reproduce phase-space properties observed in the relativistic treatment. By plotting Poincaré surfaces of section and using two recurrence methods for similar situations as in the relativistic case, we find similar tendencies in the evolution of the phase portrait with parameters (mainly with mass of the disc/ring and with energy of the orbiters), namely those characteristic to weakly non-integrable systems. More specifically, this is true for the Paczyński-Wiita and a newly suggested logarithmic potential, whereas the Nowak-Wagoner potential leads to a different picture. The potentials and the exact relativistic system clearly differ in delimitation of the phase-space domain accessible to a given set of particles, though this mainly affects the chaotic sea whereas not so much the occurrence and succession of discrete dynamical features (resonances). In the pseudoNewtonian systems, the particular dynamical features generally occur for slightly smaller values of the perturbation parameters than in the relativistic system, so one may say that the pseudo-Newtonian systems are slightly more prone to instability. We also add remarks on numerics (a different code is used than in previous papers), on the resemblance of dependence of the dynamics on perturbing mass and on orbital energy, on the difference between the Newtonian and relativistic Bach-Weyl rings, and on the relation between Poincaré sections and orbital shapes within the meridional plane.

Data from the Fermi Gamma-ray Burst Monitor satellite observatory suggested that the recently discovered gravitational wave source, a pair of two coalescing black holes, was related to a gamma-ray burst. The observed high-energy electromagnetic radiation (above 50 keV) originated from a weak transient source and lasted for about 1 second. Its localization is consistent with the direction to GW150914. We speculate about the possible scenario for the formation of a gamma-ray burst accompanied by the gravitational-wave signal. Our model invokes a tight binary system consisting of a massive star and a black hole which leads to the triggering of a collapse of the star's nucleus, the formation of a second black hole, and finally to the binary black hole merger. For the most-likely configuration of the binary spin vectors with respect to the orbital angular momentum in the GW150914 event, the recoil speed (kick velocity) acquired by the final black hole through gravitational wave emission is of the order of a few hundred km/s and this might be sufficient to get it closer to the envelope of surrounding material and capture a small fraction of matter from the remnant of the host star. The gamma-ray burst is produced by the accretion of this remnant matter onto the final black hole. The moderate spin of the final black hole suggests that the gamma-ray burst jet is powered by weak neutrino emission rather than the Blandford-Znajek mechanism, and hence explains the low power available for the observed GRB signal.