The gravitational field of static spherically symmetric bodies

The study of a previously proposed theory of gravitation [Petry, W. (1979).Gen. Rel. Grav.,10, 599; (1981).Ibid,13, 865] is continued. The field equations are given in a simple covariant form. For a perfect fluid with pressure the static spherically symmetric solutions of the gravitation theory are studied. Inertial and gravitational mass are identical. The solutions agree with the corresponding results of the theory of general relativity up to high order in the coupling constant. Under some natural conditions the solutions of a static spherically symmetric body are not singular.     

Spin effects during electron motion in an axially symmetric electromagnetic field

The spin properties of an electron due to quantization of its motion in a focusing electromagnetic field are studied. Within the framework of the complex Maslov WKB method, an explicit dependence is obtained for the quasiclassical particle energy spectrum on the spin. It is shown that for electrons in an axial channeling regime this will result in a different degree of states' stability depending on the value of the projection of the spin on the moment of rotation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 91–96, September, 1990.     

Equations of motion of test bodies in a spherically symmetric,static gravitational field

We consider a class of theories of gravity in which the motion of test particles is governed by the path equation (with respect to a general affine connection Г). When we restrict attention to a spherically symmetric, static gravitational field, the path equation is characterized by three arbitrary functions of the gravitational field (as opposed to two in the case of metric theories where Г={ }). We find that there are essentially only two constraints on the three functions by appealing to solar system experiments. Therefore, we must supplement the equation of motion with other physical laws to obtain a value for the third arbitrary function (this, of course, is not necessary in the case of metric theories). If we consider theories in which both Г andg play a physical role we find in certain circumstances that this “third” condition is sufficient to prove that the theories under investigation reduce to their “metric” form.     

On axially symmetric solutions of Einstein's field equations in matter and an example of static gravitational shielding

A model system, consisting of a thin spherical shell with radiusR and massM and a point massm at a distances>R from the center of the sphere, held fixed by an appropriate strut, is solved to ordermM. The stresses in the shell are not of the canonical Weyl type, and it is argued that the same is true for more realistic situations, e.g., rotating matter. Owing to the nonlinearity of Einstein's field equations, the field of the point mass is shielded from the interior of the shell by a factor lying between 1–3M/R and 1–2M/R, and the field outside the shell explicitly depends onR.     

Tomography in external axially symmetric field

The generalization of the Cormack algorithm for inversion of the Radon transform with axially symmetric absorption is proposed. The Radon transform is one of the main mathematical tools of optical tomography. In many technical applications, the absorption is axially symmetric. This allows one to perform the expansion of the original and its image in terms of angular harmonics, which simplifies the inversion of the transform.     

Radial-velocity distribution of electrons in an axially symmetric focusing electromagnetic field

We construct the distribution function of beams of charged particles with assigned angular momentum in an axially symmetric electromagnetic field. We find a distribution function that enables us to establish a connection between the effective size of the beam and its parameters.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 87–91, September, 1985.     

Interaction of plasma clusters with an axially symmetric magnetic field

The paper reports about measurements of the magnetic flux of a probe coil excited by a plasma cluster, moving in an axially symmetric magnetic field. The effective diamagnetic current, inductance and resistance of the cluster are derived from the dependence of the measured flux on the distance between the standard coil and the coil forming the magnetic field, as well as from the estimated main dimensions of the cluster.In conclusion the author wishes to express his thanks to Mr. J. Divíek for his devoted work in assembling the apparatus and to Mr, J. Bacílek for his work connected with the vacuum technique.     

Radiational self-polarization of electron-positron beams in an axially symmetric focusing electric field

Radiational self-polarization of an electron (positron) beam with spontaneous emission in an axially symmetric focusing electric field with a potential of the form (r)=Ur^µ is considered. The analysis is based on the solutions of the Dirac equations found in the approximation of small oscillations in the vicinity of the equilibrium radius of rotation. It is shown that the existence of self-polarization depends significantly on the structure of the field; in particular, the probability of electron transitions with spin reversal is zero when =–1.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 88–92, April, 1989.     

Massless spinning test particles in a gravitational field

The classical equations of motion of a massless spinning test particle are derived as a limiting case of Mathisson-Papapetrou equations. It is shown that when a particular supplementary condition is assumed the particle follows a null geodesic and the spin is either parallel or antiparallel to the direction of motion. Moreover, the helicity is conserved in an orientable spacetime. The equations of the propagation of the momentum vector and the spin tensor along the trajectory are given and further implications of the solution are discussed.     

Criteria for the field boundaries of an axially symmetric ultrawideband radiator

Criteria for the near and far electromagnetic fields of ultrawideband radiation are considered based on a numerical simulation. To estimate the field boundaries for ultrawideband radiation, it is proposed to use the condition of the maximum (near field) and minimum (far field) differences between the time dependences of the electromagnetic field components. The approach proposed has been approved for an axially symmetric radiator excited by voltage pulses of varied waveform and duration. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 46–50, September, 2008.     

An axially symmetric scalar field and teleparallelism

An axially symmetric scalar field is considered in teleparallel gravity. We calculate, respectively, the tensor, the vector and the axial-vector parts of torsion and energy, momentum and angular momentum in the ASSF. We find the vector parts are in the radial and \(\hat{e}_{\theta}\) directions, the axial-vector, momentum and angular momentum vanish identically, but the energy distribution is different from zero. The vanishing axial-vector part of torsion gives us the result that there occurs no deviation in the spherical symmetry of the spacetime. Consequently, there exists no inertia field with respect to a Dirac particle, and the spin vector of a Dirac particle becomes constant. The result for the energy is the same as obtained by Radinschi. Next, this work also (a) supports the viewpoint of Lessner that the Møller energy-momentum complex is a powerful concept for the energy-momentum, (b) sustains the importance of the energy-momentum definitions in the evaluation of the energy distribution of a given spacetime, and (c) supports the hypothesis by Cooperstock that the energy is confined to the region of non-vanishing energy-momentum tensor of the matter and all non-gravitational fields.     

The electrostatic and gravitational field of spherically symmetric objects

The electrostatic and gravitational fields of an extended spherically symmetric object is presented. The limit to a point-like object is discussed for Born-Infeld type of electrodynamics and it is shown, that the extreme Reissner-Nordstrøm field, where no event horizon occurs, is unphysical.     

Chaotic motion in axially symmetric potentials with oblate quadrupole deformation

By computing the Poincaré?s surfaces of section and Lyapunov exponents, we study the effect of introducing an oblate quadrupole in the dynamics associated with two generic spherical potentials of physical interest: the central monopole and the isotropic harmonic oscillator. In the former case we find saddle points in the effective potential, in contrast to the statements presented by Guéron and Letelier in [E. Guéron, P.S. Letelier, Phys. Rev. E 63 (2001) 035201]. The results we show in the second case have application in nuclear or atomic physics. In particular, we find values of oblate deformation leading to a disappearance of shell structure in the single-particle spectrum.     

轴对称导体在均匀磁场中转动时的电荷分布及其电磁场的求解方法

指出了某些文献中的问题,根据电荷守恒定律,证明了由转动磁场所导致的电场E=±v×B的散度,并非与真实的电荷体密度有本质上的关联,而只是一种相对论效应.并根据电磁场变换原理,给出了轴对称导体在均匀稳恒磁场中转动时表面电荷密度及其电磁场的求解方法,得出了在均匀稳恒磁场中转动的导体球表面电荷密度及其电磁场.     

Relativistic spinning particle in a gravitational field with torsion

A model of a relativistic spinning particle in a gravitational field with a flat metric and a constant torsion is analyzed within the framework of classical mechanics. The Lagrange equations allow an exact integration.Tomsk State Pedagogical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 50–54, November, 1993.     

也谈均匀磁场中旋转的中性轴对称导体上的电荷分布

严格证明了中性轴对称导体在均匀外磁场中旋转时,等势面为同轴圆柱面,并由电荷守恒定律证明该轴上的磁场精确等于外磁场Bo。同时还得出了该导体表面电荷密度的普遍公式。     

Power of spontaneous emission for a nonrelativistic particle in an axially symmetric magnetic field

Using the quasiclassical trajectory-coherent states method for a nonrelativistic particle moving in an axially symmetric magnetic field, we have determined the characteristics of spontaneous emission, taking into account the first quantum correction. In the special case of a constant homogeneous magnetic field, the result agrees well with previously known characteristics.Tomsk Polytechnical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 79–82, October, 1992.