Particle motion in the field of a five-dimensional charged black hole

In this paper, we have investigated the geodesics of neutral particles near a five-dimensional charged black hole using a comparative approach. The effective potential method is used to determine the location of the horizons and to study radial and circular trajectories. This also helps us to analyze the stability of radial and circular orbits. The radius of the innermost stable circular orbits have also been determined. Contrary to the case of massive particles for which, the circular orbits may have up to eight possible values of specific radius, we find that the photons will only have two distinct values for the specific radii of circular trajectories. Finally we have used the dynamical systems analysis to determine the critical points and the nature of the trajectories for the timelike and null geodesics.     

Predicting the maximum sunspot number and the associated geomagnetic activity indices a a $aa$ and A p $Ap$ for solar cycle 25

We are considering the spacetime described by the metric proposed by Mannheim and Kazanas. The effective potential and the circular orbits are discussed. The rotational velocity derived from the geodesics equation agrees with the observed flat galactic rotation curves. Finally, solutions to the Gordon equation for massless bosons evolving in this spacetime are obtained in terms of Heun general functions.

     

Geodesics and geodesic deviation in static charged black holes

The radial motion along null geodesics in static charged black hole space–times, in particular, the Reissner–Nordström and stringy charged black holes, are studied. We analyzed the properties of the effective potential. The circular photon orbits in these space–times are investigated. We found that the radius of circular photon orbits in both charged black holes are different and differ from that given in Schwarzschild space–time. We studied the physical effects of the gravitational field between two test particles in stringy charged black hole and compared the results with that given in Schwarzschild and Reissner–Nordström black holes.     

Test-particle motion in superposed Weyl fields

In a previous paper (Paper I), several superposed Weyl solutions of Einstein equations were investigated that might have some astrophysical relevance. We drew the gravitational field lines in the superposed space–times and the distortions of the Schwarzschild event horizon induced by the additional matter. Here we are concerned with the motion of free test particles in the same fields. In particular, the influence of the parameters (mass and location) of the additional sources on the positions of important circular equatorial geodesics is studied.     

Static cylindrically symmetric gravitational field with cosmological constant

We show that a class of solutions for a vacuum cylindrically symmetric gravitational field with nonvanishing cosmological constant reduce to the welknown Levi-Civita metric close to the axis. All the circular geodesics in this generalized vacuum are time like, null or space like depending on the relative magnitudes of the two parameters appearing in the solutions.For other particles moving inZ=constant plane there are some cases where the trapping of timelike and null trajectories occur, while in other cases some of the particles may orbit round the axis in a fixed zone bounded by two limiting radii.     

Geodesic study of regular Hayward black hole

This paper is devoted to study the geodesic structure of regular Hayward black hole. The timelike and null geodesics have been studied explicitly for radial and non-radial motion. For timelike and null geodesic in radial motion there exists analytical solution, while for non-radial motion the effective potential has been plotted, which investigates the position and turning points of the particle. It has been found that massive particle moving along timelike geodesics path are dragged towards the BH and continues to move around black hole in particular orbits.     

Steps for solving the radiative transfer equation for arbitrary flows in stationary space–times

We derive the radiative transfer equation for arbitrary stationary relativistic flows in stationary space–times, i.e. for steady-state transfer problems. We show how the standard characteristics method of solution developed by Mihalas and used throughout the radiative transfer community can be adapted to multidimensional applications with isotropic sources. Because the characteristics always coincide with geodesics and can always be specified by constants, direct integration of the characteristics derived from the transfer equation as commonly done in 1D applications is not required. The characteristics are known for a specified metric from the geodesics. We give details in both flat and static spherically symmetric space–times. This work has direct application in 3D simulations of supernovae, gamma-ray bursts, and active galactic nuclei, as well as in modelling neutron star atmospheres.     

On the second integrals of geodesics in the Kerr field

Qualitative analysis is given of the second integrals of the equations of geodesics of the Kerr metric expressed in the Boyer-Lindquist coordinates.     

Kerr黑洞周围束缚粒子(m≠0)的短程线

报道Kerr黑洞周围一般轨道中,静质量m≠0的束缚粒子短程线的物理性质．根据粒子运动方程,用数值计算方法得到了在轨两类粒子的存在判据和粒子的轨迹,给出了不同运动积分常数条件下,粒子短程线参数的变化规律．     

Bianchi-II Rotating World

Dynamical and kinematic properties of Bianchi-II cosmological models with rotation and expansion are investigated. Exact solutions of Einstein field equations are obtained which describe the evolution of a rotating Universe. Exact solutions of null, timelike and spacelike geodesics are constructed. Two new cosmological tests for rotating universes are discussed: cosmological lens effect and cosmological mirror effect.     

Paralleltransport and geodesic deviation in static spherically symmetric space-times

Tetrads which are parallelpropagated along time-like geodesics in static spherically symmetric spce-times are constructed. Its connection with the geodesic precession is explained. Moreover, we express the solution of the equations of geodesic deviation in terms of the Killing vectors and the fourvelocity.     

Relative chaos in stellar systems

Statistical properties of many-dimensional dynamical systems-stellar systems of different types, are investigated by means of new definition of relative chaos based on the estimation of the Ricci curvature in the direction of the velocity of geodesics. Numerical experiment is performed to calculate the Ricci and scalar curvatures for systems with equal total energy. The results of calculations enable one to obtain schematic classification of stellar systems by increasing degree of chaos.     

Stable magnetic universes revisited

Recent discovery of magnetars (B～10¹⁵ G) motivates us to consider magnetic universes in general relativity a new. A regular class of static, cylindrically symmetric pure magnetic field metrics is rederived in a different metric ansatz in all dimensions. Radial, time dependent perturbations show that for dimensions d>3 such spacetimes are stable at both near r≈0 and large radius r→∞. For d=3, however, simultaneous stability requirement at both, near and far radial distances can not be reconciled for time-dependent perturbations. We argue that this distinct property may be the cause for the absence of pure magnetic black holes in d=3. Restricted, numerical geodesics for neutral particles reveal a gravitational confinement around the center in the polar plane. Charged, time-like geodesics for d=4 are shown numerically to remain confined as well.     

Physical properties of charged Kaluza-Klein black holes

In this paper, we consider an exact vacuum solution of the Kaluza-Klein (KK) theory, which describes nonrotating KK black holes. We investigate general properties of geodesic motion in the space-time and calculate the effective potential for null geodesics. The thermodynamical quantities as well as the gravitational lensing of the solution is calculated. We illustrate that the Carter-Penrose diagram for different parameter values resembles the Schwarzschild-like, naked and charged solutions.     

Wormhole deformation of the Reissner-Nordstr?m spacetime

A radial deformation of the Reissner-Nordstr?m metric which leads to the appearance of charged, traversable wormholes is investigated. It is shown that the resulting wormholes are not covered by event horizons and physical signals can travel between the two parallel universes either way across the wormhole. The status of energy conditions and the classification of geodesics are also discussed in details.     

The microwave background and (m,Z) relations in a tilted cosmological model

The structure of the cosmic microwave background temperature is studied in the context of a Bianchi type-V tilted cosmological model. First integrals of the equations for the null geodesics are found by use of the symmetries of the model, enabling the celestial temperature distribution to be found. The quadrupole and dipole moments are calculated for some models, suggesting that the observed anisotropy in the cosmic microwave background can be understood in the context of a Bianchi type-V model of the Universe. The apparent magnitude-redshift relations are also calculated for these models.     

A Geometric Interpretation of Integrable Motions

Integrability, one of the classic issues in galactic dynamics and in general in celestial mechanics, is here revisited in a Riemannian geometric framework, where Newtonian motions are seen as geodesics of suitable -mechanical- manifolds. The existence of constants of motion that entail integrability is associated with the existence of Killing tensor fields on the mechanical manifolds. Such tensor fields correspond to hidden symmetries of non-Noetherian kind. Explicit expressions for Killing tensor fields are given for the N = 2 Toda model, and for a modified Hénon-Heiles model, recovering the already known analytic expressions of the second conserved quantity besides energy for each model respectively.     

Inertia and a fifth dimension—special relativity from a new perspective

The phenomenon of inertia is modeled by a new process, which semi-discretely changes the metrical scale of spacetime. This process explains inertia as a curved spacetime phenomenon, since all accelerating trajectories take place on geodesics of general relativity. By this approach inertial reference frames are Minkowskian manifolds imbedded in a five-dimensional space. It would imply a revised interpretation of special relativity, which preserves a universal temporal reference. If acceleration curves spacetime, it would also imply the existence of an energy-momentum tensor with net energy, which under certain conditions could become negative.