Narrow Results

We investigate the existence and stability of both the timelike and null circular orbits for a (2 + 1)-dimensional charged BTZ black hole in Einstein-nonlinear Maxwell gravity with a negative cosmological constant. The stability analysis of orbits is performed to study the possibility of chaos in geodesic motion for a special case of black hole so-called conformally invariant Maxwell spacetime. The computations of both proper time Lyapunov exponent $({\lambda }_p)$ and coordinate time Lyapunov exponent $({\lambda }_c)$ are useful to determine the stability of these circular orbits. We observe the behavior of the ratio $({\lambda }_p/{\lambda }_c)$ as a function of radius of circular orbits for the timelike case in view of different values of charge parameter. However, for the null case, we calculate only the coordinate time Lyapunov exponent $({\lambda }_c)$ as there is no proper time for massless test particles. More specifically, we further analyze the behavior of the ratio of ${\lambda }_{\mathrm{\text{Null}}}$ to angular frequency $({\mathrm{\Omega }}_c)$, so-called instability exponent as a function of charge $(q)$ and parameter related to cosmological constant $(l)$ for the particular values of other parameters.

Circular orbits are examined in static spacetimes belonging to the Weyl class of vacuum solutions which represent (nonlinear) superposition of the gravitational fields generated by certain collinear distributions of matter. In particular, solutions representing two and three Chazy–Curzon particles — all of them endowed with conical singularities — are considered. Conditions for geodesic motion in certain symmetry planes are discussed and results are summarized in a number of graphics too. All the discussion is developed in the framework of observer-dependent analysis of motion.

Parallel transport along circular orbits in orthogonally transitive stationary axisymmetric spacetimes is described explicitly relative to Lie transport in terms of the electric and magnetic parts of the induced connection. The influence of both the gravito-electromagnetic fields associated with the zero angular momentum observers and of the Frenet–Serret parameters of these orbits as a function of their angular velocity is seen on the behavior of parallel transport through its representation as a parameter-dependent Lorentz transformation between these two inner-product preserving transports which is generated by the induced connection. This extends the analysis of parallel transport in the equatorial plane of the Kerr spacetime to the entire spacetime outside the black hole horizon, and helps give an intuitive picture of how competing "central attraction forces" and centripetal accelerations contribute with gravitomagnetic effects to explain the behavior of the 4-acceleration of circular orbits in that spacetime.

The motion of test particles along circular orbits in the vacuum C metric is studied in the Frenet–Serret formalism. Special orbits and corresponding intrinsically defined geometrically relevant properties are selectively studied.

The classification of Einstein clusters based on the analysis of the stability of circular orbits according to the effective potential theory is compared with that resulting from the application of the maximum binding energy criterion. The stability properties are investigated for different choices of the energy density profile. The cases of clusters with constant energy density, those characterized by arbitrarily large values of the central gravitational redshift and clusters with Burkert-type and Navarro-Frenk-White-type energy density profiles used in the literature to model galactic halos are discussed.

A class of exact conformastatic solutions of the Einstein-Maxwell field equations is presented in which the gravitational and electromagnetic potentials are completely determined by a harmonic function only. The motion of test particles is investigated in the background of a space-time characterized by this class of solutions. We focus on the study of circular stable and unstable orbits obtained by taking account particular harmonic functions defining the gravitational potential. We show that is possible to have repulsive force generated by the charge distribution of the source. As the space-time here considered is singularity free we conclude that this phenomena is not exclusive to the case of naked singularities. Additionally, we obtain an expression for the perihelion advance of the test particles in a general magnetized conformastatic space-time.

We study the motion of neutral test particles along circular orbits in the Reissner-Nordström spacetime. We use the method of the effective potential with the constants of motion associated to the underlying Killing symmetries. A comparison between the black hole and naked singularity cases is performed. In particular we find that in the naked singularity case for r < Q²/M no circular orbits can exist, this radius plays a fundamental role in the physics of the naked singularity. For r > Q²/M and there are two stability regions together with a region where all the circular orbits are instable and a zone in which all trajectory are possible but not circular orbits, for one stability region and a region where all circular orbits are instable appear, finally for there are all stable circular orbits for r > Q²/M.

Effective potential for a class of static solutions of Kaluza-Klein equations with threedimensional spherical symmetry is studied. Test particles motion is analyzed. In attempts to read the obtained results with the experimental data, particular attention is devoted to the Schwarzschild’s limit of the four dimensional counterpart of these electromagnetic free solutions. Massive particles stable circular orbits in particular are studied, and a comparison between the well known results if the Schwarzschild’s case and those found for the static higher dimensional case is performed. A modification of the circular stable orbits is investigated in agreement with the experimental constraints.

Relevant properties of test-particle equatorial circular orbits in the Kerr–anti-de Sitter spacetimes, including their existence, stability and orientation, are briefly discussed.