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.     

Relativistic gas in a gravitational field

Equations describing the kinetics and hydrodynamics of a relativistic gas in a gravitational field are obtained using the concept of a gravitational field as a physical field in a pseudo-Euclidean space-time.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 17–20, September, 1982.     

Neutron interferometry in gravitational field with torsion

We consider the possibility of finding experimental evidence of the fifth force with the measurement of a phase shift of neutron beams via an interferometric apparatus and also a possible rotation of the polarization plane of polarized neutron beams when torsion is introduced in a gravitational field.     

Relativistic orbital perturbations in a weak gravitational field

With the general third-order equations of motion for a test particle, Synge's third-order orbital equations at great distance in the weak gravitational field generated by a massive body are derived. The body has an axis of symmetry around which is rotating steadily. The results found for the advance of perihelion using first integrals of motion for the general equations show that the effect due to the inner stress of the body can be derived for orbits with inclination with respect to the equator of the body. Then, by means of the variation of the parameters method, we obtain with the equations at great distance the corresponding perturbations on the elements of such orbits in the field considered. These perturbations result to be of second order with regard to the mass of the body (the basis of the approximation).     

Relativistic particle dynamics in external gravitational fields

Using the Riemann metric for event space, which leads to Newtonian mechanics at nonrelativistic velocities and not necessarily weak gravitational fields, the dynamics of relativistic particles in external gravitational fields are considered. Trajectories, laws of motion, and equations of light rays are found in homogeneous and Newtonian fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 56–61, October, 1977.In conclusion the authors thank Yu. G. Pavlenko for his evaluation of the results and valuable advice.     

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.     

Relativistic particle in a traveling magnetic field

A Hamiltonian formalism is applied to derive an exact solution to the equation of motion of a charged particle in the electromagnetic field of a traveling current wave. The particle motion is studied in a monochromatic magnetic field and in the traveling jump-like front of the magnetic field, and the wave mechanism for betatron acceleration is analyzed. It is shown that, in each of these situations, a charged particle can be accelerated simultaneously in both the longitudinal and transverse directions.     

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.     

Relativistic quantum particle in a time-dependent homogeneous field

A model of the relativistic quantum particle under the action of a time-dependent force is considered. This exactly solvable model is realized in the one-dimensional relativistic configurational x-space and is described by the finite-difference equation. The momentum p-space is one-dimensional Lobachevsky space. We have explicitly constructed the wave functions and propagators for this model in both x- and p-representations. We have also found a solution of a definite class of partial differential and finite-difference equations, which can be interpreted as the operator identities.     

Relativistic quantum particle in a homogeneous external field

The model of the relativistic quantum particle in a homogeneous external field is proposed. This model is realized in the one-dimensional relativistic configurational x-space and is described by the finite-difference equation. The momentum p-space in our case is the one-dimensional Lobachevsky space. We have found the wave functions and propagator for the model under study in both x- and p-representations.     

Relativistic kinetic equations for inelastically interacting particles in a gravitational field

The relativistic canonical formalism is used to construct the kinetic equations for a gas in a gravitational field, whose particles interact with one another via numerous inelastic collisions. Boltzmann's H-theorem is proved for T-invariant interactions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 19–23, August, 1983.     

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.     

A generalized lovelock theorem for the gravitational field with torsion

The U₄ field equations are uniquely determined up to three parameters if they are assumed to be polynomial in metric, torsion and their derivatives, respectively, and free of new fundamental constants. The parameters can be fixed by means of the equivalence principle.     

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.     

Relativistic kinetics of an anisotropic plasmalike medium with damping in a field of gravitational radiation

An exact solution is obtained for the general relativistic kinetic equation with model collision integral that describes the motion of an initially homogeneous anisotropic plasma in a field of plane gravitational waves (GW) of arbitrary amplitude and polarization. The amplitude of the induced current is calculated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 70–74, December, 1984.     

Stochastic quantization method for spinning particles in a gravitational plane wave field

The exact and analytic Green functions for spinning relativistic particles in interaction with a gravitational plane wave field are obtained within the Stochastic Quantization Method of Parisi and Wu. We have separated the classical calculations from those related to the quantum fluctuations. The problem has been solved by using a perturbative treatment via the Langevin equation relying on phase and configuration spaces formulation.      

Behavior of effective charges in a quantum-field-theory model in an external gravitational field with torsion

Renormalization group equations are obtained for the parameters of nonminimal coupling of matter with an external gravitational field with torsion. The asymptotical behavior of these parameters in the short-distance limit is studied. The asymptotical conformal invariance of the theory is established.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 58–62, December, 1985.