The behavior of the gravitational field near the initial singularity

The ultralocal representation of the canonically quantized gravitational field is used to obtain the evolution of coherent states in the immediate neighborhood of the singularity. It is shown that smearing functions play the role of classical fields since they correspond to cosmological solutions around the singularity. A special class of ultralocal coherent states is shown to contain the essential aspects of the dynamics of the system when we choose a simple representation for the field operators of the theory. When the ultralocality condition is broken a conjecture will be made about the quantum evolution of coherent states in the classical limit.     

Massive spin-two particle in a gravitational field

The spin-two particle is described by a symmetric tensorh subject to the subsidiary conditionsh = h =0. Their covariant generalization and the wave equation have been obtained directly from the Eulerian variational equations by algebraic methods only. In addition to the tensor fieldh a symmetric third-rank tensor = as well as a vector fieldA have been added, neither of which enter in the final result. The Lagrangian function is taken as a linear sum of all combinations which can be constructed from these functions, as well as terms involving the curvature tensor and its two possible contractions. Variation with respect toh , andA independently gives the Euler equations. Combining the various trace equations and choice of arbitrary constants yields the subsidiary conditions, while the Euler equations themselves give the connection between the auxiliary functions and the tensorh as well as the generalization of the wave equationD D h + 2R h -R h -R h +g R h +Rh =m ² h Finally, variation with respect tog yields the energy-momentum tensor.     

On the gravitational field of a massless particle

The gravitational field of a massless point particle is first calculated using the linearized field equations. The result is identical with the exact solution, obtained from the Schwarzschild metric by means of a singular Lorentz transformation. The gravitational field of the particle is nonvanishing only on a plane containing the particle and orthogonal to the direction of motion. On this plane the Riemann tensor has a -like singularity and is exactly of Petrov typeN.This work was supported in part by Fonds zur Förderung der Wissenschaftlichen Forschung.     

The Clifford bundle and the nature of the gravitational field

In this paper we formulate Einstein's gravitational theory with the Clifford bundle formalism. The formalism suggests interpreting the gravitational field in the sense of Faraday, i.e., with the field residing in Minkowski spacetime. We succeeded in discovering the condition for this interpretation to hold. For the variables that play the role of the gravitational field in our theory, the Lagrangian density turns out to be of the Yang-Mills type (with an auto-interaction plus gauge-fixing terms). We give a brief comparison of our theory with other field theories of the gravitational field in the flat Minkowski spacetime.     

Behavior of a charged particle in a schwarzschild field

The influence of the De Witt self-action force on the motion of and electromagnetic emission from a charged particle in a Schwarzschild field is considered. It is shown that a charged particle in a Schwarzschild field is equivalent to a neutral particle of the same mass in a certain Reissner-Nordstrom field. A relationship is found between the power of the electromagnetic emission from an accelerated charge and the power of the thermal emission generated in a reference frame with the same acceleration at the event horizon. The quantum-mechanical problem of the motion of and emission from a charge in the field of a minihole is considered. Wave functions, the energy spectrum, and the widths of quasi-stationary levels are found with allowance for the De Witt self-action force. It is shown that the latter is important for large charges, when the solution becomes oscillatory. "Brainstorm" Little Science and Technology Enterprise. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 75–82, July, 1998.     

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.     

On the behavior of an oscillator clock near the singularity of a gravitational field

In 1975 Møller tried to show that the general relativistic concept of standard time or proper time would lose its physical meaning in the vicinity of singularities of a gravitational field [1]. His treatment of a classical harmonic oscillator clock falling into a singularity is checked in the present paper and is found to be insufficient to prove the above statement. A relativistic clock model is given to ensure the reasonable physical meaning of proper time.     

Brownian motion of a charged particle in a magnetic field

We develop and numerically illustrate an exact solution of the multivariate, stochastic, differential equations that govern the velocity and position of a charged particle in a plane normal to a uniform, stationary, magnetic field. The equations self-consistently incorporate the Lorentz force into an Ornstein-Uhlenbeck collision model. Properties of the solution in the infinite dissipation limit are explored and the spectral energy density function is found     

Strong field gravitational lensing by a stringy charged black hole

In this paper, we study gravitational lensing of magnetically charged black hole of string theory as a strong field approximation for the supermassive black hole at the center of NGC4486B. We evaluate light deflection angle numerically, from which we obtain magnifications, Einstein rings and observables for the relativistic images. Finally, we explore time delay between relativistic images when they are on the same as well as opposite side of the lens. It is concluded that charge parameter plays a prominent role in the strong gravitational lensing.     

Relativistic motion of a free particle in a uniform gravitational field

The problem of the motion of a free particle in a uniform gravitational field is considered. A relativistic solution based on the assumption that the motion is a consequence of the curvature of spacetime is obtained. The results are compared with various results based on the assumption that spacetime is flat in a region in which the gravitational field is uniform. In the curved spacetime approach, if a particle is projected from a point in a uniform gravitational field, the vertical distance covered by the particle in infinite coordinate time is infinite, but the horizontal distance covered and the elapsed proper time of the particle are finite. If spacetime is assumed to be flat and the gravitational motion of a particle a consequence of a relativistic force proportional to the relative mass of the particle, then the results obtained for the motion of a particle in a uniform gravitational field are close to the curved spacetime results. All other assumptions, including the assumption that the motion of a particle in a uniform gravitational field is equivalent to the motion of a particle in a uniformly accelerating frame of reference, lead to results in serious disagreement with the curved spacetime results.     

The charged particle radiation field in the electrodynamics of moving media

We solve Sommerfeld's problem of the accelerated charge radiation in a uniformly moving simple medium.     

On the motion of a charged particle in a helical magnetic field

The rectilinear motion of a charged particle in a helical magnetic field is analyzed. Averaging methods are used as a device to study the equations of motion. The averaged system is constructed and analyzed to find the adiabatic invariants, from which the basic parameters of the focusing system can be calculated.     

The nature of the initial singularity

We consider the initial singularity in the universe as isotropic and with a strength the same as that of the singularity in the density function. We consider the effect of this initial singularity on a particle falling into it in the future at a high speed. This gives a precise understanding of the fate of particles falling into the final singularity in the future of aK=+1 Friedmann-Le Maitre-Robertson-Walker universe.     

Propagator for a charged particle in a time-dependent electromagnetic field

We first show that the propagator of a charged particle in a time-dependent electromagnetic field, obtained by choosing the vector and scalar potentials to be in static symmetric gauge, is related to the propagator of a one-dimensional particle under a time-dependent perturbative force and with generalized memory. For the case of a constant magnetic field, the latter can then be evaluated exactly with the help of a gaussian integral. Our new results are in agreement with the well-known results of simpler cases.     

Chaos feature of test particle in the gravitational field with a quadrupole

In this paper we investigate the dynamics of a test particle in the gravitational field with a quadrupole. By constructing Poincaré sections for different values of the parameters and initial conditions, we find a chaotic evolution. From these Poincaré sections, we further confirm that the chaotic evolution of the test particle originates from the quadrupole.     

Screening of a charged particle field in rarefied ionized gas

A self-consistent field of a charged micron-size particle placed in a rarefied ionized gas is created by both free ions moving along infinite trajectories and trapped ions moving in closed orbits. The character of screening of the particle field is analyzed under dynamic conditions in a nonequilibrium plasma where the temperature (or the mean energy) of electrons greatly exceeds the ion temperature. Under these conditions, trapped ions are generated in a restricted region of the particle field where the transitions between closed ion orbits resulting from resonant charge exchange dominate. This leads to a higher number density of trapped ions compared to that of free ions. The parameters of the self-consistent field of the particle and ions are found when free or trapped ions determine the screening of the particle field, and a similarity law is established for a simultaneous variation of the number density of plasma particles and the particle size. In dusty plasmas of the Solar System, which result from the interaction of the solar wind with dust, formation of trapped ions increases the plasma number density compared to that in the solar wind.     

Motion of a charged particle in a uniform rotating magnetic field

The motion of a charged particle in a rotating, uniform magnetic field is investigated. Expressions are obtained for the domains of steady-state motion and for the particle trajectories. The investigation includes a treatment of conditions specifying the particle localization within the bounded space domain.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 7–11, December, 1976.     

Motion of a particle in a gravitational field in the special theory of relativity

The equations of motion for a particle moving in a gravitational field considered in planar spacetime are derived. A simplified form of these equations is obtained for the particular case of a centrosymmetric field subject to a simplifying assumption concerning the structure of the potential of a field with this sort of symmetry. Under this assumption the displacement of the perigee of the planets amounts to five-sixths of the value given by the general theory of relativity.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 48–52, March, 1977.