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Roman Plyatsko

Publications and source records attributed to Roman Plyatsko.

At least 19 recordsLinked to original sources

Samuil Kaplan and the development of astrophysical research at the Lviv University (dedicated to the 100th anniversary of his birth)

Samuil Kaplan (1921-1978) was a productive and famous astrophysicist. He was affiliated with a number of scientific centers in different cities of former Soviet Union. The earliest 13 years of his career, namely in the 1948-1961 years, he worked in Lviv University in Ukraine (then it was called the Ukrainian Soviet Socialist Republic). In the present paper, the Lviv period of his life and scientific activity is described on the basis of archival materials and his published studies. Kaplan arrived in Lviv in June 1948, at the same month when he obtained the degree of Candidate of science. He was a head of the astrophysics sector at the Astronomical Observatory of the University, was a professor of department for theoretical physics as well as the founder and head of a station for optical observations of artificial satellites of Earth. He was active in the organization of the astronomical observational site outside of the city. During the years in Lviv, Kaplan wrote more than 80 articles and 3 monographs in 9 areas. The focus of his interests at that time was on stability of circular orbits in the Schwarzschild field, on white dwarf theory, on space gas dynamics, and cosmic plasma physics, and turbulence, on acceleration of cosmic rays, on physics of interstellar medium, on physics and evolution of stars, on cosmology and gravitation, and on optical observations of Earth artificial satellites. Some of his results are fundamental for development of theory in these fields as well as of observational techniques. The complete bibliography of his works published during the Lviv period is presented. Respective scientific achievements of Samuil Kaplan are reviewed in the light of the current state of research in these areas.

astro-ph.CO

On physics of a highly relativistic spinning particle in the gravitational field

The Mathisson-Papapetrou equations are used for investigations of influence of the spin-gravity coupling on a highly relativistic spinning particle in Schwarzschild's field. It is established that interaction of the particle spin with the gravitomagnetic components of the field, estimated in the proper frame of the particle, causes the large acceleration of the spinning particle relative to geodesic free fall. As a result the accelerated charged spinning particle can generate intensive electromagnetic radiation when its velocity is highly relativistic. The significant contribution of the highly relativistic spin-gravity coupling to the energy of the spinning particle is analyzed.

gr-qc

Nonequatorial circular orbits of spinning particles in the Schwarzschild-de Sitter background

In this paper analytical solutions of the Mathisson-Papapetrou equations that describe nonequatorial circular orbits of a spinning particle in the Schwarzschild-de Sitter background are studied, and the role of the cosmological constant is emphasized. It is shown that generally speaking a highly relativistic velocity of the particle is a necessary condition of motion along this type of orbits, with an exception of orbits locating close to the position of the static equilibrium, where low velocities are possible as well. Depending on the correlation between the spin orientation of the particle and its orbital velocity some of the possible nonequatorial circular orbits exist due to the repulsive action on the particle caused by the spin-gravity coupling and the others are caused by the attractive action.Here values of the energy of the particle on the corresponding orbits are also analyzed.

gr-qc

Highly relativistic spin-gravity-$Λ$ coupling

The effects of highly relativistic spin-gravity coupling in the Schwarzschild-de Sitter background which follow from the Mathisson-Papapetrou equations are investigated. The dependence of gravitoelectric and gravitomagnetic components of gravitational field on the velocity of an observer which is moving in Schwarzschild-de Sitter's background is estimated. The action of gravitomagnetic components on a fast moving spinning particle is considered. Different cases of the highly relativistic circular orbits of a spinning particle which essentially differ from the corresponding geodesic orbits are described.

gr-qc

Antigravity: Spin-gravity coupling in action

The typical motions of a spinning test particle in Schwarzschild's background which show the strong repulsive action of the highly relativistic spin-gravity coupling are considered using the exact Mathisson-Papapetrou equations. An approximated approach to choice solutions of these equations which describe motions of the particle's proper center of mass is developed.

gr-qc

Solutions of Mathisson-Papapetrou equations for highly relativistic spinning particles

Different types of essentially nongeodesic motions of highly relativistic spinning particles in Schwarzschild's and Kerr's background which follows from the Mathisson-Papapetrou (MP) equations are considered. It is shown that dependently on the correlation of signs of the spin and the particle's orbital velocity the spin-gravity coupling acts as a significant repulsive or attractive force. Numerical estimates for electrons, protons, and neutrinos in the gravitational field of black holes are presented. The correspondence between the general relativistic Dirac equation and MP equations is discussed. It is stressed that for the highly relativistic motions the adequate supplementary condition for the MP equations is the Mathisson-Pirani condition. In the following it is important to study the possible role of the highly relativistic spin-gravity coupling in astrophysics, cosmology, and high energy physics.

gr-qc

Highly relativistic spin-gravity coupling for fermions

Descriptions of highly relativistic fermions in a gravitational field in the classical (nonquantum) and quantum approaches are discussed. The results following from the Mathisson-Papapetrou equations for a fast spinning particle in Schwarzschild's and Kerr's background are considered. Numerical estimates for electron, proton and neutrino in the gravitational field of black holes are presented.The general relativistic Dirac equation is analyzed from the point of view it is using for the adequate description of highly relativistic fermions in a gravitational field, in the linear and nonlinear spin approximation. It is necessary to have some corrected Dirac equation for a highly relativistic fermion with strong spin-gravity coupling.

gr-qc

Highly relativistic circular orbits of spinning particle in the Kerr field

The Mathisson-Papapetrou equations in Kerr's background are considered. The region of existence of highly relativistic planar circular orbits of a spinning particle in this background and dependence of the particle's Lorentz $γ$-factor on its spin and radial coordinate are investigated. It is shown that in contrast to the highly relativistic circular orbits of a spinless particle the corresponding orbits of a spinning particle are allowed in much wider space region. Some of these orbits show the significant attractive action of the spin-gravity coupling on a particle and others are caused by the significant repulsive action. Numerical estimates for electrons, protons and neutrinos in the gravitational field of black holes are presented.

gr-qc

Highly relativistic spinning particle in the Schwarzschild field: Circular and other orbits

The Mathisson-Papapetrou equations in the Schwarzschild background both at Mathisson-Pirani and Tulczyjew-Dixon supplementary condition are considered. The region of existence of highly relativistic circular orbits of a spinning particle in this background and dependence of the particle's orbital velocity on its spin and radial coordinate are investigated. It is shown that in contrast to the highly relativistic circular orbits of a spinless particle, which exist only for $r=1.5 r_g(1+δ)$, $0<δ\ll 1$, the corresponding orbits of a spinning particle are allowed in a wider space region, and the dimension of this region significantly depends on the supplementary condition. At the Mathisson-Pirani condition new numerical results which describe some typical cases of non-circular highly relativistic orbits of a spinning particle starting from $r>1.5 r_g$ are presented.

gr-qc

Can Mathisson-Papapetrou equations give clue to some problems in astrophysics?

First, we stress that for correct description of highly relativistic fermions in a gravitational field it is necessary to have an equation which in the limiting transition to the classical (non-quantum) case corresponds to the exact Mathisson-Papapetrou equations. According to these equations the spin in general relativity is Fermi-transported, and the parallel transport of spin is realized only in some approximation. The traditional general-relativistic Dirac equation (1929) is based on the parallel transported spinors and does not ensure the correspondent transition. Second, because in the range of very high velocity (close to the speed of light) of a spinning particle relative to the Schwarzschild or Kerr sources the Mathisson-Papapetrou equations have the solutions which reveal that the spin-gravity interaction acts as a strong antigravity force, we suppose that this fact can be useful for explanation some astrophysical phenomena. Some association with the OPERA results is possible.

gr-qc

Mathisson-Papapetrou-Dixon equations in the Schwarzschild and Kerr backgrounds

A new representation, which does not contain the third-order derivatives of the coordinates, of the exact Mathisson-Papapetrou-Dixon equations, describing the motion of a spinning test particle, is obtained under the assumption of the Mathisson-Pirani condition in a Kerr background. For this purpose the integrals of energy and angular momentum of the spinning particle as well as a differential relationship following from the Mathisson-Papapetrou-Dixon equations are used. The form of these equations is adapted for their computer integration with the aim to investigate the influence of the spin-curvature interaction on the particle's behavior in the gravitational field without restrictions on its velocity and spin orientation. Some numerical examples for a Schwarzschild background are presented.

gr-qc

Highly relativistic spinning particle starting near $r_{ph}^{(-)}$ in a Kerr field

Using the Mathisson-Papapetrou-Dixon (MPD) equations, we investigate the trajectories of a spinning particle starting near $r_{ph}^{(-)}$ in a Kerr field and moving with the velocity close to the velocity of light ($r_{ph}^{(-)}$ is the Boyer-Lindquist radial coordinate of the counter-rotation circular photon orbits). First, as a partial case of these trajectories, we consider the equatorial circular orbit with $r=r_{ph}^{(-)}$. This orbit is described by the solution that is common for the rigorous MPD equations and their linear spin approximation. Then different cases of the nonequatorial motions are computed and illustrated by the typical figures. All these orbits exhibit the effects of the significant gravitational repulsion that are caused by the spin-gravity interaction. Possible applications in astrophysics are discussed.

gr-qc

On a Representation of Mathisson-Papaetrou-Dixon Equations in the Kerr Metric

New representation of the exact Mathisson-Papapetrou-Dixon equations at the Mathisson-Pirani condition in the Kerr metric which does not contain the third-order derivatives of the coordinates of a spinning particle is obtained. For this purpose the integrals of energy and angular momentum of the spinning particle as well as a differential relationship following from the Mathisson-Papapetrou-Dixon equations are used. The form of these equations is adapted for their computer integration with the aim of further investigations of the influence of the spin-curvature interaction on the particle's behavior in the gravitational field without restrictions on its velocity and spin orientation.

gr-qc

On common solutions of Mathisson equations under different conditions

In the context of investigations of possible highly relativistic motions of a spinning particle in the gravitational field, which can be described by the Mathisson equations under different supplementary condition, we analyze the circular orbits in a Schwarzschild field. The very orbits most clearly demonstrate the effect of the gravitational spin-orbit interaction on the particle's motion. It is shown that the Mathisson equations under the Frenkel-Mathisson and Tulczyjew-Dixon conditions have the common solutions describing the highly relativistic circular orbits in the region $r=3M(1+δ), |δ|\ll 1$. These orbits essentially differ from the geodesic circular orbits in the same region, particularly by the value of the particle's energy on the corresponding orbits.

gr-qc

Mathisson Equations: Non-Oscillatory Solutions in a Schwarzschild Field

The Mathisson equations under the Frenkel-Mathisson supplementary condition are studied in a Schwarzschild field. The choice of solutions, which describe the motions of the proper center of mass of a spinning test particle, is discussed, and the calculation procedure for highly relativistic motions is proposed. The very motions are important for astrophysics while investigating possible effects of the gravitational spin-orbit interaction on the particle's world line and trajectory.

gr-qc

Some partial solutions of Mathisson-Papapetrou equations in a Schwarzschild field

The analytical and numerical solutions of the Mathisson-Papapetrou equations under the Mathisson-Pirani supplementary condition describing highly relativistic (ultrarelativistic) motions of a spinning particle in a Schwarzschild field are investigated. The known condition S/mr<<1, which is necessary for a test particle, holds on all these solutions. The explicit expressions for the non-equatorial circular orbits, in particular for the space boundaries of the region of existence of these orbits, are obtained. The dynamics of the deviation of a spinning particle from the equatorial ultrarelativistic circular orbit with r=3M caused by the non-zero initial value of the radial particle's velocity is studied. It is shown in the concrete cases that spin can considerable influence the shape of an ultrarelativistic trajectory, as compared to the corresponding geodesic trajectory, for the short time, less than the time of one or two revolutions of a spinning particle around a Schwarzschild mass.

gr-qc

Fermi-transported spinor and Dirac equation in general relativity

The Fermi transport of the Dirac spinor is considered as a generalization of the parallel transport of this spinor which was introduced by V. Fock and D. Ivanenko (1929). The possible structure of the new variant of the general-relativistic Dirac equation based on the Fermi transport is discussed.

gr-qc