Issue 1/2013

ABSTRACTS:

UDK 530.145.7; 514.764.2

STATIONARY BOUND STATES OF SPIN-HALF PARTICLES IN THE KERR AND KERR – NEWMAN GRAVITATIONAL FIELDS / M. V. Gorbatenko, V. P. Neznamov
We prove the possibility of existence of stationary bound states of spin-half probe particles for the Kerr and Kerr-Newman gravitational fields using Сhadrasekhar’s Hamiltonian. If the Hilbert condition is satisfied, , bound states of Dirac particles with a real discrete energy spectrum can exist both for particles above the surface of the outer ergosphere of the Kerr and Kerr-Newman fields, and for particles staying under the internal «event horizon» (the Cauchy horizon) and, at the same time, under the surface of the inner «ergosphere».
In this case, the surfaces of the outer and inner ergospheres play the role of infinitely high potential barriers. Spin-half quantum-mechanical particles cannot cross the ergosphere surfaces of the Kerr and Kerr-Newman fields.
Based on the results of this study, we can assume that there exists a new type of rotating collapsars, for which the Hawking radiation mechanism is not present.
The results of this study can lead to a revision of some concepts of the standard cosmological model related to the evolution of the universe and interaction of rotating collapsars with surrounding matter.

UDK 530.145.7; 514.764.2
STATIONARY BOUND STATES OF SPIN-HALF PARTICLES IN THE REISSNER – NORDSTR?M GRAVITATIONAL FIELD / M. V. Gorbatenko, V. P. Neznamov
We prove the possibility of existence of stationary bound states of spin-half particles in the Reissner-Nordstr?m gravitational field using a self-conjugate Hamiltonian with a flat scalar product of wave functions.
Bound states of Dirac particles with a real discrete energy spectrum can exist both for particles above the external «event horizon», and for particles under the internal «event horizon», or the Cauchy horizon.
The Gilbert condition  leads to a boundary condition such that components of the vector of current density of Dirac particles are zero near the «event horizons».
Based on the results of this study, we can assume that there exists a new type of charged collapsars, for which the Hawking radiation is not present.
The results of this study can lead to a revision of some concepts of the standard cosmological model related to the evolution of the universe and interaction of charged collapsars with surrounding matter.

UDK 530.145.7; 514.764.2
ABSENCE OF THE NON-UNIQUENESS PROBLEM OF THE DIRAC THEORY IN A CURVED SPACETIME. SPIN-ROTATION COUPLING IS NOT PHYSICALLY RELEVANT / M. V. Gorbatenko, V. P. Neznamov
As opposed to Arminjon’s statements, in this work we again prove the absence of the non-uniqueness problem of the Dirac theory in a curved and flat spacetime and illustrate this with a number of examples. Dirac Hamiltonians in arbitrary, including time-dependent, gravitational fields uniquely determine physical characteristics of quantum-mechanical systems irrespective of the choice of the tetrad fields. Direct spin-rotation coupling that occurs with a certain choice of tetrads does not manifest itself in final physical characteristics of the systems and therefore does not represent a physically relevant effect.

UDK 551.551
NUMERICAL STUDY OF THE EFFECT OF INITIAL PERTURBATION SPECTRUM ON THE DEVELOPMENT OF GRAVITATIONAL TURBULENT MIXING / Yu. V. Yanilkin, V. P. Statsenko, O. G. Sinkova, O. N. Chernyshova, V. B. Rozanov, N. V. Zmitrenko
The development of gravitational turbulent mixing by variations of the initial harmonic spectrum and random 3D perturbations on a light/heavy material interface is studied numerically. The results are compared with appropriate ones, which authors obtained earlier on robust mesh with random perturbations on interface. Simulations were carried out using 3D TREK code.

UDK 532.529
SCAVENGING OF ATMOSPHERIC GASEOUS IMPURITIES FROM ARBITRARY DYNAMIC SOURCE THAT ACTING IN THE SUB-CLOUD LAYER / V. N. Piskunov, D. V. Tsaplin
The scavenging process of gaseous impurities in the sub-cloud layer taking into account the impurity evaporation from droplets and the atmospheric turbulent diffusion is considered. The problem is solved by the method of splitting into physical processes in which the dynamics of the impurities washout is treated separately – against the background of the atmospheric diffusion and transfer. Thus, these processes create a dynamic background source of impurity in the sub-cloud layer. The general solution of the kinetic equations of scavenging for the source with an arbitrary background distribution was obtained. Analysis of this solution was carried out for two limiting cases: slow and fast changing with time sources (compared with the process of washout). The results of the illustrative calculations are presented and the practical guidelines on the calculation of scavenging rate for numerical systems are adduced.