The source of the Kerr geometry

It is shown that the volume Casimir effect for ultradense matter gives a negative contribution to the energy density and determines the specific structure of the energy-momentum tensor of the source of the Kerr metric. The source is assumed to have the form of a thin relativistic disk. The connection between the Kerr metric and models of strings and bags is discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 80–86, May, 1988.In conclusion the author sincerely thanks P. I. Pronin and V. M. Mostepanenko, and also Prof. D. D. Ivanenko and the participants of his seminar for useful discussions supporting the work and for making preprints available.     

New nonlinear intensity Kerr effect in the polar geometry

The problem of the electromagnetic wave reflection on the second optical harmonic from a semi-infinite optically isotropic magnetic medium is considered for the uniform magnetization direction corresponding to the polar Kerr effect. In the first approximation in magnetization, the method of Green’s tensor functions is used to derive expressions for the complex amplitudes of the wave fields for the incidence of s-and p-polarized waves (as well as of their superposition) on the medium. It is shown that, in the latter case, the nonlinear polar Kerr effect is of the intensity type. The dependences of the intensity effect on the angle of incidence of the inducing wave and on the angle of its polarization, which were obtained in numerical experiments, are presented. A comparative analysis of the linear and nonlinear intensity Kerr effects is carried out.     

Nonlinear intensity-related magneto-optical Kerr effects in the planar geometry

The reflection of an electromagnetic wave at the second-harmonic frequency from a semi-infinite optically isotropic magnetic medium for the directions of uniform magnetization corresponding to the meridional and equatorial Kerr effects is considered. Using the Green’s tensor function technique, in the first approximation in magnetization, the expressions for complex amplitudes of the field are obtained for the s and p polarizations of the incident beam and their superpositions. It is shown that in the latter case, the meridional effect becomes intensity-related. Dependences of the intensity-related meridional and equatorial Kerr effects on the angle characterizing polarization of the pump wave are obtained by numerical calculations. A comparative analysis of the linear and nonlinear Kerr effects is made.     

On a quadratic first integral for the charged particle orbits in the charged Kerr solution

Associated with the charged Kerr solution of the Einstein gravitational field equation there is a Killing tensor of valence two. The Killing tensor, which is related to the angular momentum of the field source, is shown to yield a quadratic first integral of the equation of the motion for charged test particles.The research reported herein has been supported in part by the National Science Foundation, grants GP-8868, GP-20023, and GU-1598; the Air Force Office of Scientific Research, grant 903-67; the National Aeronautics and Space Administration, grant 44-004-001; and the Westinghouse Corporation.     

Non-commutative geometry inspired higher-dimensional charged black holes

We obtain a new, exact, solution of the Einstein's equation in higher dimensions. The source is given by a static spherically symmetric, Gaussian distribution of mass and charge. The resulting metric describes a regular, i.e. curvature singularity free, charged black hole in higher dimensions. The metric smoothly interpolates between Reissner–Nordström geometry at large distance, and de Sitter spacetime at short distance. Thermodynamical properties of the black hole are investigated and the form of the Area Law is determined. We study pair creation and show that the upper bound on the discharge time increases with the number of extra dimensions.     

Motion of a test particle in a Kerr field with fluctuating perturbations

The motion of a stochastic test particle in the field of a Kerr black hole is discussed in the approximation of Brownian interaction. The probability distribution of the position of orbits with respect to the latitudinal angle is found, and the bifurcation values of their parameters are established. The fluctuational instability of the orbits characteristic of the critical regimes of the motion is investigated, and the properties of some statistical characteristics of the system are determined.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 77–82, April, 1982.     

An approximation scheme for scalar waves in a Kerr geometry

An approximation scheme, analogous to ones previously considered for the Schwarzschild and Reissner-Nordström geometries, is applied to scalar waves in a Kerr geometry. Spectral curves of transmission coefficient for monochromatic, axially symmetric scalar waves imploding on a rotating black hole are calculated using the approximation scheme.Research supported in part by the Natural Sciences and Engineering Council of Canada.     

Electromagnetic emission of a strongly charged oscillating droplet

Analytical expressions for electric field in the vicinity of an oscillating strongly charged droplet of nonviscous conducting liquid and intensity of electromagnetic radiation are derived in the linear approximation with respect to perturbation amplitude of the droplet surface. Order-of-magnitude estimations of the radiation intensity are presented. The intensity of electromagnetic radiation of a ball lightning that can be simulated using a charged droplet is not related to the surface oscillations.     

细胞骨架微管中水分子Kerr效应对电磁场辐射的影响

微管是细胞骨架的主要组成成分和功能组件,其中充满了属于Kerr介质的液体水。本文运用量子场论路径积分方法,研究微管中水分子与电磁场的相互作用。为了考虑Kerr效应,在系统的哈密顿量中引入电磁场的非谐项。我们给出了含有Kerr非线性项的电磁辐射运动方程,进而讨论了Kerr效应对电偶极子集体辐射的影响。     

Charged particle motion in an electromagnetic field on Kerr background geometry

In this paper we study the trajectories of charged particles in an electromagnetic field superimposed on the Kerr background. The electromagnetic fields considered are of two types: (i) a dipole magnetic field with an associated quadrupole electric field, (ii) a uniform magnetic field. The contribution of the background geometry to the electromagnetic field is taken through the solutions of Petterson and Wald respectively. The effective potential is studied in detail for ther-motion of the particles in the equatorial plane and the orbits are obtained. The most interesting aspect of the study is the illustration of the effect of inertial frame dragging due to the rotation of the central star. This appears through the existence of nongyrating bound orbits at and inside the ergo surface. The presence of the magnetic field seems to increase the range of stable orbits, as was found in a previous study involving the Schwarzschild background.     

Electromagnetic energy and momentum from a charged particle

We compute the flux of the stress-energy tensor across a tube surrounding the world line of a charged particle. By slight modifications of the definition of the Coulomb energy-momentum, the resulting expression contains the radiation reaction term (proportional to the square of the four-acceleration) but not the Schott term (proportional to the derivative of the acceleration). The equation of motion for the particle derived from this expression implies a variable rest mass.     

Equations of motion and orbit perturbations of a neutral particle in a quasi-isotropic Kerr metric

In this paper, using a quasi-isotropic from the Kerr metric, we have deduced the equations of motion of a neutral test particle in the gravitational field of a spherical homogeneous rotating body. The perturbation equations of the particle's orbit have also been derived.On leave from Shanghai Observatory, China     

Electromagnetic fields and potentials generated by massless charged particles

We provide for the first time the exact solution of Maxwell’s equations for a massless charged particle moving on a generic trajectory at the speed of light. In particular we furnish explicit expressions for the vector potential and the electromagnetic field, which were both previously unknown, finding that they entail different physical features for bounded and unbounded trajectories. With respect to the standard Liénard–Wiechert field the electromagnetic field acquires singular δ$\delta$-like contributions whose support and dimensionality depend crucially on whether the motion is (a) linear, (b) accelerated unbounded, (c) accelerated bounded. In the first two cases the particle generates a planar shock-wave-like electromagnetic field traveling along a straight line. In the second and third cases the field acquires, in addition, a δ$\delta$-like contribution supported on a physical singularity-string attached to the particle. For generic accelerated motions a genuine radiation field is also present, represented by a regular principal-part type distribution diverging on the same singularity-string.     

Electromagnetic radiation due to nonlinear oscillations of a charged drop

The nonlinear oscillations of a spherical charged drop are asymptotically analyzed under the conditions of a multimode initial deformation of its equilibrium shape. It is found that if the spectrum of initially excited modes contains two adjacent modes, the translation mode of oscillations is excited among others. In this case, the center of the drop’s charge oscillates about the equilibrium position, generating a dipole electromagnetic radiation. It is shown that the intensity of this radiation is many orders of magnitude higher than the intensity of the drop’s radiation, which arises in calculations of the first order of smallness and is related to the drop’s charged surface oscillations.