About the singularity criterion in general relativity

The metric in vacuum is found for the case of a spherical charged dust source. It is shown that a dead zone occurs in the vacuum, impenetrable to light or test particles. All singularities resulting from theorems about geodesic lines, are located in the dead zone and do not represent a physical problem for the theory. The infinite-density type singularities may be absent inside matter-filled zone.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 94–99, 1987.     

Limitations due to the spontaneous emission of low-frequency photons on the applicability of the Newtonian description of particle motion in a gas

It is shown that the spontaneous emission of low-frequency photons in collision of atoms and molecules in a gas is very rapidly, in several free-transit intervals, radically changes the trajectories and the order of the collisions of the particles as compared with the predictions of the equations of classical mechanics.     

Stability of a plane conducting fluid layer under convection in a vertical magnetic field

The nonlinear convective instability of a plane horizontal conducting fluid layer placed in a uniform vertical magnetic field is studied [1]. A similar problem was previously considered in [2] but with allowance only for so-called weakly nonlinear third-order effects. In the present paper attention is concentrated on the study of the finite-amplitude instability mechanisms associated with the "hard" excitation of vibrations. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 23–28, January–February, 1998.     

Three-dimensional waves in a boundary layer

As is known [1], two-dimensional waves develop in the boundary layer and then become three-dimensional waves with increase of the Reynolds number R. Since Squire [2] has shown that the linear growth of three-dimensional waves is more intense than that of the two-dimensional, it is natural that the behavior of three-dimensional waves in the boundary layer is explained by nonlinear intersection [3], However, Gaster [4] has noted that although disturbances which increase with time are usually considered, experimentally we observe disturbances which grow in space. (Squire's proof does not extend to this case.) It has been shown that the spatially growing disturbances cannot explain the occurrence of the three-dimensional waves (in the linear formulation).The author wishes to thank his scientific advisor G. I. Petrov and also A. A. Zaitsev for valuable discussions of the study.     

Quantum field theory overcomes Einstein's objections against quantum mechanics

It is shown that if zero-point oscillations are assumed to exist, quantum field theory will lack the determinism of classical physics. Scientific Research Institute for Nuclear Physics, Moscow University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 71–74, May, 1996.     

Stability of unsteady rectilinear plane-parallel ideal fluid flow

The stability of unsteady rectilinear plane-parallel ideal fluid flow is solved by the modified Rayleigh method [1, 2]. The numerical results apply to the so-called shear layers that form in the boundary layer prior to breakdown. The corresponding amplification factors and the most hazardous wavenumbers are found. It is shown that an analog of the Squire theorem is valid for the shear layers. In justifying the crude approximation of the initial profile, the Rayleigh method yields the exact solution for the limiting problem. A strong contraction of the class of possible initial values is not essential for finding the critical characteristics.The author thanks G. I. Petrov for his continued interest and guidance in this study.