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.     

Motion of coarse drops of binary concentrated solutions in a nonuniformly heated ternary gaseous mixture: A theory

For coarse drops of binary concentrated solutions with the double phase transition that move in a ternary gaseous mixture via thermophoresis, a theory including thermal diffusion effects is elaborated. The drops consist of water with ethanol dissolved in it. Numerical estimates are made and plots are constructed for the rate of thermophoresis of drops with radii 5, 10, and 15 μm at different ethanol concentrations with and without allowance for volume thermal diffusion.     

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.     

One-dimensional finite motion of a particle in the field of a weak gravitational wave

The Hamiltonian formalism of classical mechanics can be used effectively to describe the motion of a particle (including a massless one) along a segment of material that is in a nonsteady gravitational field. The problem of applying this formalism to the detection of gravitational waves using a Michelson or Fabry—Perot interferometer is considered. The existence of a phase shift of an electromagnetic wave due to the interaction of the electromagnetic and gravitational fields is noted. Moscow State Aviation Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 13–17, August, 1997.     

Resonance luminescence of a nonuniformly heated dense vapor

The thermal luminescence spectra of a dense, nonuniformly heated resonance medium (sodium vapor) are investigated experimentally under conditions when the resonance corrections to the relative permittivity are not small compared to unity and the photon mean free path is comparable to the wavelength of the radiation. The shape of the recorded spectra agrees well with a previously developed general theory of resonance radiation transfer which predicts a strong asymmetry of the spectra. The prospects for performing more-sensitive measurements in order to make a quantitative check of the theoretically predicted anomalous intensity (an order of magnitude higher than in the standard theory of resonance radiation transfer) of the radiation from a dense nonuniform medium are discussed. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 1, 15–19 (10 January 1997)     

String corrections to the motion of a particle in the gravitational field of a black hole

The low-energy effective action, quadratic with respect to the Riemann tensor, of string theory is used to study the motion of a test particle in the gravitational field of a black hole.V. I. Ul'yanov-Lenin Kazan State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 83–85, January, 1994.     

Charged particle motion in a medium along an electromagnetic wave

The solution of the relativistic equation of motion is discussed for a charged particle interacting with an electromagnetic wave in a medium.     

Quantum states of the neutrino in a nonuniformly moving medium

The modified Dirac equation for the neutrino in a material medium and its solution for a nonuniform motion of the medium with a velocity gradient along a certain direction are examined in the present paper. This formulation of the problem is analogous to the problem of electron motion in a constant uniform magnetic field. This is manifested through a similar character of particle wave functions that in both cases describe the states with circular orbits. A new mechanism of confinement of low-energy neutrinos in fast-rotating dense astrophysical objects is predicted based on this property of the wave functions. As an example of their application, a process of spin light ( SL_v) of neutrino is examined in this configuration of matter. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 90–96, August, 2007.     

On the non-radiating motion of a charged particle

The most general class of the electric and magnetic fields such that a charged particle moving in this field will not radiate is obtained. Apart from suitably orientated constant fields, it includes some special varying (but steady) fields.     

On the thermophoretic motion of a heated spherical drop in a viscous liquid

Expressions for the force and velocity of the thermophoretic motion of a spherical drop in a viscous liquid are derived for arbitrary temperature differences between the surface of the drop and regions away from it. The temperature dependence of the viscosity is taken into account in the form of an exponential-power series.     

Internal electric field distribution within a micro-cylinder-shaped particle suspended in an absorbing gaseous medium

The present study is concerned with photophoresis of a microsized long cylinder-shaped particle suspended in an absorbing gas medium. To facilitate the analysis, an infinite cylinder subjected to an intensive light beam is considered as the physical model. The electromagnetic energy can be absorbed by the particle and turned into thermal energy heating surface unevenly, which results in a net momentum transfer between gas molecules and the particle to drive particle in photophoretic motion. Effects of the governing parameters on the absorbed energy distribution in the cylindrical particle are investigated. The results demonstrate that increasing either the radius or absorptivity of the cylinder enhances the energy absorbed on the illuminated side and tends to generate positive photophoresis; while an increase in the refractivity of the particle tends to enhance the internal electric field intensity and shift the absorption peak on the shaded side toward the particle center. Increase in medium absorptivity reduces the energy reaching at the particle, which significantly degrades the level of energy absorption and therefore weakens the photophoretic mobility of the particle. It is also found that, at the same conditions, the source function peaks in long cylinder-shaped particles are generally lower than those in spheres due to the weaker light refraction of the cylindrical shape.     

On the motion of a uniformly heated drop in a viscous liquid under gravity

The motion of a uniformly heated spherical drop under gravity is theoretically studied within the Stokes approximation. The Stokes and Hadamard-Rybchinsky formulas are generalized so that the temperature dependence of the viscosity can be found in a wide temperature range. Also, the drag force and the velocity of gravity fall are calculated for an arbitrary temperature difference between the surface of the drop and distant points.     

On the motion of a particle with anisotropic mass

On the basis of the hypothesis that particle mass is anisotropic rather than isotropic, we investigate the relativistic motion of a particle within the framework of flat space-time. Assuming that the mass anisotropy is associated with the photon cloud of the particle, we argue that the self-energy of a particle is of the order of magnitude |δ m/M ₀|?0.0005, for which conventional quantum electrodynamics, however, gives an infinite value.