We investigate the motion of test particles in the gravitational field of a static naked singularity generated by a mass distribution with a quadrupole moment. We use the quadrupole metric ($q$ metric) which is the simplest generalization of the Schwarzschild metric with a quadrupole parameter. We study the influence of the quadrupole on the motion of massive test particles and photons and show that the behavior of the geodesics can drastically depend on the values of the quadrupole parameter. In particular, we prove explicitly that the perihelion distance depends on the value of the quadrupole. Moreover, we show that an accretion disk on the equatorial plane of the quadrupole source can be either continuous or discrete, depending on the value of the quadrupole. The inner radius of the disk can be used in certain cases to determine the value of the quadrupole parameter. The case of a discrete accretion is interpreted as due to the presence of repulsive gravity generated by the naked singularity. Radial geodesics are also investigated and compared with the Schwarzschild counterparts.

We present a stationary generalization of the static q-metric, the simplest generalization of the Schwarzschild solution that contains a quadrupole parameter. It possesses three independent parameters that are related to the mass, quadrupole moment and angular momentum. We investigate the geometric and physical properties of this exact solution of Einstein’s vacuum equations, and show that it can be used to describe the exterior gravitational field of rotating, axially symmetric, compact objects.

We present a method for generating exact interior solutions of Einstein’s equations in the case of static and axially symmetric perfect-fluid spacetimes. The method is based upon a transformation that involves the metric functions as well as the density and pressure of the seed solution. In the limiting vacuum case, it reduces to the Zipoy-Voorhees transformation that can be used to generate metrics with multipole moments. All the metric functions of the new solution can be calculated explicitly from the seed solution in a simple manner. The physical properties of the resulting new solutions are shown to be completely different from those of the seed solution.

Magnetic fields surrounding black holes are responsible for various astrophysical phenomena related to accretion processes and relativistic jets. Depending on the source, the configuration of the field lines may differ significantly, affecting the trajectories of charged particles and the corresponding observables. Usually, the magnetic fields around black holes are modeled within a single source or current generating the field. However, magnetic fields can have more than a single origin, being a combination of different fields, such as, e.g., that of an accretion disk and external large-scale or Galactic ones. In this paper, we propose a combined magnetic field solution given by the superposition of the uniform and Blandford-Znajek split-monopole magnetic fields in a strong gravity regime of the Schwarzschild black hole. We show that when the combined magnetic field components are aligned, the resulting field is of a paraboloidal jetlike shape. Such a configuration is supported by relativistic jet observations and is often utilized in general relativistic magnetohydrodynamical simulations. In the opposite orientation of the two field components, we observe looplike field structures magnetically connecting the black hole with an accretion disk and the magnetic null points, which can be related to the regions of magnetic reconnection. In the combined magnetic field configurations, we analyze the dynamics of charged particles, study their stability conditions, and find the locations of stable off-equatorial structures close to the symmetry axis. Finally, we consider an ionization of Keplerian accretion disk as a particular scenario of particle scattering. From the numerical experiments, we conclude that charged particles in the jetlike combination show a strong tendency to escape from the black hole, which is not observed in the case of individual fields. In contrast, the looplike combination supports accretion of charged particles into the black hole.

Dilatonic black hole dyon-like solutions are overviewed in the gravitational 4D model with a scalar field, two 2-forms, two dilatonic coupling constants λ i ≠ 0, i = 1, 2, obeying λ1 ≠ − λ2, and the...

We derive a particular approximate solution of Einstein equations, describing the gravitational field of a mass distribution that slightly deviates from spherical symmetry. The deviation is described by means of a quadrupole parameter that is responsible for the appearance of a curvature singularity, which is not covered by a horizon. We investigate the motion of test particles in the gravitational field of this naked singularity and show that the quadrupole parameter affects the properties of Schwarzschild trajectories. By investigating radial geodesics, we find that no effects of repulsive gravity are present. We interpreted this result as indicating that repulsive gravity is non-linear effect.