A third-order approximation for time delay of light propagation in the equatorial plane of Kerr black hole

The rotation effect of the gravitational source such as Kerr black hole on the time delay of light propagation has been studied in detail. Although it belongs to the second order, the magnitude of rotation effect may be smaller than that of the third-order effect of mass. In this paper, we calculate the time delay of the propagation of light in the equatorial plane of a Kerr black hole to the third order analytically. It is found that the third-order effect of mass is larger than the rotation effect when the magnitude of impact factor $|b| < \frac{120-5\pi }{16}\frac{M^3}{J}+M$ , with $M$ and $J$ being the mass and angular momentum of black hole. The total third-order effects on the time delay are also examined.     

Motion of the charged particles off the equatorial plane of a Kerr black hole in an electromagnetic field

Charged particle orbits off the equatorial plane of a Kerr black hole in an external electromagnetic field is studied, both for dipole as well as uniform magnetic field. Particles are found to get trapped by the magnetic field if the initial value of the parallel velocity is small. Bending of the field lines in the vicinity of the hole and the consequent trapping of the particles in an otherwise uniform magnetic field indicates the significance of general relativistic effects in such cases.     

Flag-dipole and flagpole spinor fluid flows in Kerr spacetimes

Flagpole and flag-dipole spinors are particular classes of spinor fields that has been recently used in different branches of theoretical physics. In this paper, we study the possibility and consequences of these spinor fields to induce an underlying fluid flow structure in the background of Kerr spacetimes. We show that flag-dipole spinor fields are solutions of the equations of motion in this context. To our knowledge, this is the second time that this class of spinor field appears as a physical solution, the first one occurring as a solution of the Dirac equation in ESK gravities.     

Spinning Test Particles as Locally Nonrotating Observers in Kerr Spacetime

We derive a class of exact solutions of Mathisson-Papapetrou equations of motion for spinning test particles. The world lines of the particles are those of the so-called locally non-rotating observers in Kerr spacetime.     

Nonexistence of conformally flat slices in Kerr and other stationary spacetimes

It is proved that stationary solutions to the vacuum Einstein field equations with a nonvanishing angular momentum have no Cauchy slice that is maximal, conformally flat, and nonboosted. The proof is based on results coming from a certain type of asymptotic expansion near null and spatial infinity--which also show that the development of Bowen-York-type data cannot have a development admitting a smooth null infinity--and from the fact that stationary solutions do admit a smooth null infinity.     

The circular loop equation of a cosmic string in Kerr–de Sitter spacetimes

The equation of motion of cosmic string loops in Kerr–de Sitter spacetimes is derived. Having solved the equation numerically, we find that the loops can evolve except for very small ones.     

赤道面磁层顶位形的磁流体力学模拟研究

磁层顶位置和形状的动态特征描绘是地球物理和空间物理研究的难点之一.文章基于太阳风-磁层-电离层耦合的全球磁流体力学（MHD）数值模拟,运用电流密度极大法确定磁层顶位形,并具体研究两种典型太阳风动压（D_p）和几种不同行星际磁场的z分量（B_z）条件下,地球赤道面上方磁层顶动态特征.模拟结果显示,磁层顶日下点高度r₀主要由D_p控制.随着D_p增加,磁层顶被压缩,r₀显著减小.相同D_p条件下,在B_z由南向（B_z<0）逐渐减小,并转为北向（B_z>0）逐渐增大的过程中,r₀缓慢增大.不同条件下,磁层项张角φ变化较小,反映了赤道面磁层顶结构的相似性.与Shue98低纬磁层顶经验模型比较,MHD模拟能再现磁层顶日下点位置r₀对D_p的响应,而r₀随B_z变化的饱和性仅出现在低速太阳风条件下.MHD模拟和经验模型的磁层项张角φ差别小于2.5°,但模拟显示φ随B_z的变化趋势并非简单线性关系.     

The regularity of static spherically cylindrically and plane symmetric spacetimes at the origin

We find the necessary and sufficient conditions for the regularity of all scalar invariants polynomial in the Riemann tensor at the origin of spherically, cylindrically and plane symmetric static spacetimes under the assumption that the metric functions are sufficiently smooth there. These conditions turn out to be simple enough to allow a check for regularity by inspection.     

Spin-1/2 and spin-3/2 field solutions in plane wave spacetimes

We have found two non-trivial massless Dirac and two massive Rarita–Schwinger solutions in plane wave spacetimes. The first order symmetry operator transforming one of the massless Dirac solution to the other is constructed. The only non-vanishing spinor bilinear generated by the standard spinor basis is obtained and algebraic relations between the induced parallel forms are demonstrated. It is also seen that the spin-3/2 norm of the Rarita–Schwinger solutions enforces to the massless sector.     

Note on Kantowski-Sachs spacetimes

It is shown that a portion of de Sitter space can be expressed in the formds ²=dt ²–A ² (t)dr ²–B ²(t)(d ²+sin ² d ²). It follows that it is a Kantowski-Sachs spacetime, according to the usual definition. This disproves the statement sometimes seen in the literature that all Kantowski-Sachs spacetimes are anisotropic.     

Investigation of the trajectories of a magnetized particle in the equatorial plane of a magnetic dipole

The movement of a magnetized particle in the equatorial plane of a magnetic dipole is investigated. Analysis and classification of trajectory types for such particles are made. It is shown that eight different trajectory types are possible, which depend on the particle’s energy and on the orientation of its magnetic dipole moment. This permits the use of an axial magnetic field to move a magnetized particle in any point of the magnetic equatorial plane.     

Note on the completeness of spacetimes

Three formally different definitions of completeness for normal hyperbolic manifolds are discussed and shown to be inequivalent.     

Stability of maximal hypersurfaces in spacetimes: new general conditions and application to relevant spacetimes

We obtain new simple sufficient conditions to ensure the stability and strong stability of maximal hypersurfaces (without boundary) immersed in an arbitrary spacetime. Several applications to maximal hypersurfaces in a spatially open or closed spacetime endowed with an infinitesimal causal symmetry are also given.     

Kerr效应对T-C模型中原子布居数的影响

应用全量子理论，研究了Kerr介质中双模压缩真空场与耦合二能级原于相互作用系统原子布居差的时间演化规律，讨论了初始压缩因子、介质与辐射场的耦合强度对原子布居时间演化的影响。结果表明，随着Kerr效应的加强，原于布居的崩塌一回复周期变短，以至消失，振荡幅度减小。     

Acausality in Gowdy spacetimes

We present a parametrization of T ³ and S ¹ × S ² Gowdy cosmological models which allows us to study both types of topologies simultaneously. We show that there exists a coordinate system in which the general solution of the linear polarized special case (with both topologies) has exactly the same functional dependence. This unified parametrization is used to investigate the existence of Cauchy horizons at the cosmological singularities, leading to a violation of the strong cosmic censorship conjecture. Our results indicate that the only acausal spacetimes are described by the Kantowski-Sachs and the Kerr-Gowdy metrics.     

Beyond the speed of light on Finsler spacetimes

As a prototypical massive field theory we study the scalar field on the recently introduced Finsler spacetimes. We show that particle excitations exist that propagate faster than the speed of light recognized as the boundary velocity of observers. This effect appears already in Finsler spacetime geometries with very small departures from Lorentzian metric geometry. It switches on for a sufficiently large ratio of the particle four-momentum and mass, and is the consequence of a modified version of the Coleman–Glashow velocity dispersion relation. The momentum dispersion relation on Finsler spacetimes is shown to be the same as on metric spacetimes, which differs from many quantum gravity models. If similar relations resulted for fermions on Finsler spacetimes, these generalized geometries could explain the potential observation of superluminal neutrinos claimed by the Opera Collaboration.     

Symmetry breaking in dynamical spacetimes

The behaviour of scalar electrodynamics under symmetry breaking by the Higgs mechanism is studied in a class of dynamical spacetimes—those having a Bianchi type I symmetry—which includes the spatially flat Robertson-Walker spacetimes. The Einstein equations are used to obtain the effective Lagrangian, from which it is shown thateither the gauge field does not become massive during symmetry breaking (in marked contrast with the case in which the background spacetime is static),or the symmetry breaking chooses not only a direction in the phase space of the Higgs field, but also a spatial direction in the spacetime sections.