A compact stellar-mass object inspiralling onto a massive black hole deviates from geodesic motion due to radiation-reaction forces as well as finite-size effects. Such post-geodesic deviations need to be included with sufficient precision into wave-form models for the upcoming space-based gravitational-wave detector LISA. I present the formulation and solution of the Hamilton-Jacobi equation of geodesics near Kerr black holes perturbed by the so-called spin-curvature coupling, the leading order finite-size effect. In return, this solution allows to compute a number of observables such as the turning points of the orbits as well as the fundamental frequencies of motion. This result provides one of the necessary ingredients for waveform models for LISA and an important contribution useful for the relativistic two-body problem in general.

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.