Based on the Newman-Janis algorithm, the Ay\'on-Beato-Garc\'\ia spacetime metric [Phys. Rev. Lett. 80, 5056 (1998)

Properties of the Schwarzschild–de Sitter and Schwarzschild–anti-de Sitter spacetimes are characterized by three phenomena, namely, by the “effective potential” of the motion of test particles and photons, the photon escape cones, and the embedding diagrams of $t=\mathrm{const}$ sections of central planes of both the ordinary and optical reference geometry of these spacetimes. The phenomena are related to the corresponding phenomena of the Schwarzschild spacetime, and differences caused by the asymptotic structure of the spacetimes with a nonzero cosmological constant are discussed. The properties of the embedding diagrams of the optical geometry are related to the dynamical behavior of test particles. The limits of the embeddability of the optical geometry are given and compared with the limits on the outer radius of the interior solutions of Einstein’s equations with a nonzero cosmological constant for static, spherically symmetric configurations of uniform density. It is shown that, contrary to the pure Schwarzschild case, these limits do not fully coincide for repulsive cosmological constants.

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 $M\sim {10}^{10}{M}_{\odot }$ surrounded by sufficiently strong magnetic field with $B\sim {10}^4$ 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 study the motion of charged particles in the field of a rotating black hole immersed into an external asymptotically uniform magnetic field, focusing on the epicyclic quasicircular orbits near the equatorial plane. Separating the circular orbits into four qualitatively different classes according to the sign of the canonical angular momentum of the motion and the orientation of the Lorentz force, we analyze the circular orbits using the so-called force formalism. We find the analytical solutions for the radial profiles of velocity, specific angular momentum, and specific energy of the circular orbits in dependence on the black-hole dimensionless spin and the magnetic field strength. The innermost stable circular orbits are determined for all four classes of the circular orbits. The stable circular orbits with an outward-oriented Lorentz force can extend to radii lower than the radius of the corresponding photon circular geodesic. We calculate the frequencies of the harmonic oscillatory motion of the charged particles in the radial and vertical directions related to the equatorial circular orbits and study the radial profiles of the radial, ${\omega }_{\mathrm{r}}$; vertical, ${\omega }_{\theta }$; and orbital, ${\omega }_{\varphi }$, frequencies, finding significant differences in comparison to the epicyclic geodesic circular motion. The most important new phenomenon is the existence of toroidal charged particle epicyclic motion with ${\omega }_{\mathrm{r}}\sim {\omega }_{\theta }\gg {\omega }_{\varphi }$ that could occur around retrograde circular orbits with an outward-oriented Lorentz force. We demonstrate that for the rapidly rotating black holes the role of the “Wald induced charge” can be relevant.

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

We construct regular rotating black hole and no-horizon spacetimes based on the recently introduced spherically symmetric generic regular black hole spacetimes related to electric or magnetic charge under nonlinear electrodynamics coupled to general relativity that for special values of the spacetime parameters reduce to the Bardeen and Hayward spacetimes. We show that the weak and strong energy conditions are violated inside the Cauchy horizons of these generic rotating black holes. We give the boundary between the rotating black hole and no-horizon spacetimes and determine the black hole horizons and the boundary of the ergosphere. We introduce the separated Carter equations for the geodesic motion in these rotating spacetimes. For the most interesting new class of the regular spacetimes, corresponding for magnetic charges to the Maxwell field in the weak field limit of the nonlinear electrodynamics, we determine the structure of the circular geodesics and discuss their properties. We study the epicyclic motion of a neutral particle moving along the stable circular orbits around the “Maxwellian” rotating regular black holes. We show that epicyclic frequencies measured by the distant observers and related to the oscillatory motion of the neutral test particle along the stable circular orbits around the rotating singular and regular Maxwellian black holes are always smaller than ones in the Kerr spacetime.