Equilibrium States in the Quadruple–Kerr Solution

The extended quadruple–Kerr metric is used to consider equilibrium states of four collinear Kerr particles. We explain our previous failure to solve numerically the full set of the balance equations, and we derive a self–consistent system of the axis conditions leading to the equilibrium of all four constituents which can be black holes or hyperextreme objects. The equilibrium configurations obtained in this paper exhibit similar features with those occurring in the systems of two Kerr particles, for instance, the balance of four Kerr black holes with positive masses does not seem possible. Equilibrium states of two identical compound Kerr objects are also discussed.     

Local field effects in magneto-optics of two-dimensional arrays of ferromagnetic nanoparticles

A theory of the polar magneto-optical Kerr effect in a layer of small ferromagnetic particles has been developed in the framework of the Green’s function method of electrodynamics. The manifestation in magneto-optics of the local field effect, which is initiated by the contribution to the effective field of dipole moments induced in particles, has been studied in terms of the model of a square lattice of ferromagnetic ellipsoids. The magneto-optical Kerr effect stimulated under normal incidence of a linearly polarized electromagnetic wave on a layer of particles magnetized perpendicular to the layer plane has been analyzed. The dependence of the Kerr rotation angle in an array of ellipsoidal Co particles embedded in the transparent dielectric CaF₂ on the light frequency, the parameters of the ellipsoidal particles, and the lattice period (concentration of the magnet in the layer) has been studied numerically. It has been shown that, within a broad (2.0–4.5 eV) spectral range, the local field effect studied as a function of increasing concentration of Co particles in the layer manifests itself in the reversal of the sign of the Kerr rotation compared to that observed in a single ellipsoid or a solid Co film.     

Tunnelling Effect of Massive Particles from Kerr Black Holes

In this paper, we extend Parikh’s (massless particles) and Zhang’ work to massive particles’ Kerr black hole tunnelling. By treating the massive particle as de Broglie wave, we calculate the emission rates of the particles across the event horizon of the Kerr black holes. Our result is successful and is in agreement with the form of the massless particles.     

Spontaneous creation of massive spin half particles by a rotating block hole

The techniques of second quantization in Kerr metric for the scalar and neutrino (massless) fields are extended to the massive spin half case. The normal modes of Dirac field in Kerr metric are obtained in Chandrasekhar’s representation and the field is quantized as usual by imposing equal-time anti-commutation relations. The vacuum expectation value of energy-momentum tensor is evaluated asymptotically, leading to the result that a Kerr black hole spontaneously creates, in addition to scalar and neutrino quanta, massive Dirac particles in the classical superradiant modes.     

Repulsive effects in steady axisymmetric fields

In this paper the repulsive effects in the Kerr and Kerr--Newman fields are discussed. The contributions made by all parameters of the fields and test particles to the repulsive effects are also discussed, and the accretive effect on interstellar dust, i.e. the distribution of dust is calculated. The discussion is also carried out on the slow rotation of the Kerr field in which the effect is related to the positions and velocities of the particles and the orientations of their trajectories as well.     

Planckian Scattering from Kerr Black Holes: Eikonal and Beyond

Planckian scattering of particles with angular momenta is studied by describing them as sources of the Kerr metric. In the shock wave formalism, it is found that the angular momenta do not contribute to the scattering amplitude in the eikonal limit. This is confirmed by using the wave equation of the test particle in the Kerr background.     

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.     

Bohmian Trajectories for Kerr–Newman Particles in Complex Space-Time

Complexified Liénard–Wiechert potentials simplify the mathematics of Kerr–Newman particles. Here we constrain them by fiat to move along Bohmian trajectories to see if anything interesting occurs, as their equations of motion are not known. A covariant theory due to Stueckelberg is used. This paper deviates from the traditional Bohmian interpretation of quantum mechanics since the electromagnetic interactions of Kerr–Newman particles are dictated by general relativity. A Gaussian wave function is used to produce the Bohmian trajectories, which are found to be multi-valued. A generalized analytic continuation is introduced which leads to an infinite number of trajectories. These include the entire set of Bohmian trajectories. This leads to multiple retarded times which come into play in complex space-time. If one weights these trajectories by their natural Bohmian weighting factors, then it is found that the particles do not radiate, that they are extended, and that they can have a finite electrostatic self energy, thus avoiding the usual divergence of the charged point particle. This effort does not in any way criticize or downplay the traditional Bohmian interpretation which does not assume the standard electromagnetic coupling to charged particles, but it suggests that a hybridization of Kerr–Newman particle theory with Bohmian mechanics might lead to interesting new physics, and maybe even the possibility of emergent quantum mechanics.     

Kerr effect caused by an electric current in a weakly ionized gas

The anisotropy of the velocity distribution caused by an electric current in a fluid leads to a molecular alignment via the non-spherical interaction. This alignment implies a birefringence proportional to the square of the applied electric field just as the ordinary Kerr effect. The kinetic theory of this phenomenon is presented for a lorentzian mixture, viz. a gas of few light charged linear molecules and of many heavy optically isotropic particles. The current-induced contribution to the Kerr effect turns out to be much larger than the contribution which stems from the usually considered orienting influence of the electric field on anisotropic molecules.     

磁流体制备及性质研究

采用化学共沉淀法制备了纳米Fe3O4磁性颗粒,将其均匀分散在载液中获得磁流体.给出了表征所制备样品的宏观和微观特性图谱,探究了样品的磁热效应、法拉第效应和克尔效应,并制作了磁流体薄膜显示器.通过对磁流体样品的分析,获得其最佳的油酸钠包裹量为0.0216g/mL,样品颗粒小,稳定性高,磁热效应明显.研究发现磁流体薄膜的透射率随磁场变化明显,测量费尔德系数时必须考虑透射率的影响.磁流体样品存在异常克尔信号.     

Dirac粒子的Hawking蒸发

在Kerr背景时空中求解Dirac方程是一个长期没有解决的问题。1976年Chandrasekhar成功地找到了Kerr背景时空中静止质量不为零的Dirac方程的退耦和分离变量的量子方程。本文在此基础上,在近似极端Kerr黑洞的事件视界附近找到了静止质量不为零的Dirac方程的解,并成功地导出了Hawking热谱公式,从而解决了Dirac粒子在Kerr黑洞的Hawking蒸发问题。 关键词：     

Origin of the resonant optical Kerr nonlinearity in Cd(S,Se)-doped glasses and related topics

After having reported preliminary results related to saturation, we first theoretically consider the various mechanisms contributing to the resonant optical Kerr effect in Cd(S, Se)-doped glasses. We obtain the expression for the expected effective susceptibility in different possible cases. This nonlinearity is studied experimentally using optical-phase conjugation in the low-intensity regime. We show that, by time resolving the nonlinear response of such glasses having experienced various degrees of photodarkening, we can clearly assess the origin of the resonant optical Kerr effect in these materials. Usually, a combination of a fast free-carrier contribution due to particles without traps and of a slow trapped-carrier one due to particles with traps is observed. For the free-carrier contribution, induced absorption is observed to be almost as important as absorption saturation. We also report frequency-dependent measurements and discuss the change in absorption spectrum and the increase of the nonradiative decay rate that accompany darkening.     

Hawking Radiation of Dirac Particles in a Variable-Mass Kerr Space-Time

The Hawking effect of Dirac particles in a variable-mass Kerr space-time is investigated by using a method called as the generalized tortoise coordinate transformation. The location and the temperature of the event horizon of the non-stationary Kerr black hole are derived. It is shown that the temperature and the shape of the event horizon depend not only on the time but also on the angle. However, the Fermi–Dirac spectrum displays a residual term which is absent from that of Bose–Einstein distribution.     

Radiation force exerted on nanometer size non-resonant Kerr particle by a tightly focused Gaussian beam

We calculate the radiation force that is exerted by a focused continuous-wave Gaussian beam of wavelength λ on a non-absorbing nonlinear particle of radius a ? 50λ/π. The refractive index of the mechanically-rigid particle is proportional to the incident intensity according to the electro-optic Kerr effect. The force consists of two components representing the contributions of the electromagnetic field gradient and the light scattered by the Kerr particle. The focused intensity distribution is determined using expressions for the six electromagnetic components that are corrected to the fifth order in the numerical aperture (NA) of the focusing objective lens. We found that for particles with a < λ/21.28, the trapping force is dominated by the gradient force and the axial trapping force is symmetric about the geometrical focus. The two contributions are comparable with larger particles and the axial trapping force becomes asymmetric with its zero location displaced away from the focus and towards the beam propagation direction. We study the trapping force behavior versus incident beam power, NA, λ, and relative refractive index between the surrounding liquid and the particle. We also examine the confinement of a Kerr particle that exhibits Brownian motion in a focused beam. Numerical results show that the Kerr effect increases the trapping force strength and significantly improves the confinement of Brownian particles.     

Nonthermal radiation of rotating black holes

The nonthermal radiation of a Kerr black hole is considered as the tunneling of particles being produced through an effective Dirac gap. In the leading semiclassical approximation, this approach is also applicable to bosons. Our semiclassical results for photons and gravitons are consistent with those obtained previously. For neutrinos, the result of our complete quantum-mechanical calculation is about twice as large as the previous one.     

Chaos and dynamics of spinning particles in Kerr spacetime

We study chaos dynamics of spinning particles in Kerr spacetime of rotating black holes use the Papapetrou equations by numerical integration. Because of spin, this system exists many chaos solutions, and exhibits some exceptional dynamic character. We investigate the relations between the orbits chaos and the spin magnitude S, pericenter, polar angle and Kerr rotation parameter a by means of a kind of brand new Fast Lyapulov Indicator (FLI) which is defined in general relativity. The classical definition of Lyapulov exponent (LE) perhaps fails in curve spacetime. And we emphasize that the Poincaré sections cannot be used to detect chaos for this case. Via calculations, some new interesting conclusions are found: though chaos is easier to emerge with bigger S, but not always depends on S monotonically; the Kerr parameter a has a contrary action on the chaos occurrence. Furthermore, the spin of particles can destroy the symmetry of the orbits about the equatorial plane. And for some special initial conditions, the orbits have equilibrium points.     

Thermodynamics inducing massive particles’ tunneling and cosmic censorship

By calculating the change of entropy, we prove that the first law of black hole thermodynamics leads to the tunneling probability of massive particles through the horizon, including the tunneling probability of massive charged particles from the Reissner–Nordström black hole and the Kerr–Newman black hole. Novelly, we find the trajectories of massive particles are close to that of massless particles near the horizon, although the trajectories of massive charged particles may be affected by electromagnetic forces. We show that Hawking radiation as massive particles tunneling does not lead to violation of the weak cosmic-censorship conjecture.     

The Lorentz-Dirac equation in complex space-time

A hypothetical equation of motion is proposed for Kerr–Newman particles. It’s obtained by analytic continuation of the Lorentz-Dirac equation into complex space-time. A new class of “runaway” solutions are found which are similar to zitterbewegung. Electromagnetic fields generated by these motions are studied, and it’s found that the retarded (and advanced) times are multi-sheeted functions of the field points. This leads to non-uniqueness for the fields. With fixed weighting factors for these multiple roots, the solutions radiate. However, position dependent weighting factors can suppress radiation and allow non-radiating solutions. Motion with external forces are also considered, and radiation suppression is possible there too. These results are relevant for the idea that Kerr–Newman solutions provide insight into elementary particles and into emergent quantum mechanics. They illustrate a type of nascent wave-particle duality and complementarity in a purely classical field theory. Metric curvature due to gravitation is ignored.     

Nonconservation of the net current of Dirac particles in Tolman-Bondi and Robertson-Walker geometries

A straightforward calculation shows that, in contrast to what happens for the Dirac equation in the Kerr metric, the net current of particles is not conserved in the case of the Dirac equation in the Tolman-Bondi and Robertson-Walker space-times.     

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.