Calculation of the Relativistic Correction in Terms of the Oscillator Representation

A procedure is proposed for the calculation of the corrections associated with the relativistic motion and spin interaction of particles in a system of a few bodies. The relativistic corrections for the Coulomb and Cornell potentials are determined from the relativistic generalization of the Schrödinger equation. The slope of the Regge trajectory and the masses of mesons are calculated taking the relativistic correction into account.     

On relativistic thermodynamics

The thermodynamics of moving bodies is developed from first principles. To do this, it is necessary to augment the laws of thermodynamics with a new principle, which asserts the impossibility of thermal equilibrium between bodies in relative motion. Clausius' theorem is generalized to heat flow between moving systems, and leads naturally to the identification of heat and temperature as Lorentz scalars. The formulation of relativistic statistical mechanics is carried out and the correspondence with classical quantities is made. The quantum distribution laws are generalized to the relativistic case, and are found to differ from their accepted relativistic form.     

Relativistic closed-form Hamiltonian for many-body gravitating systems in the post-Minkowskian approximation

The Hamiltonian for a system of relativistic bodies interacting by their gravitational field is found in the post-Minkowskian approximation, including all terms linear in the gravitational constant. It is given in a surprisingly simple closed form as a function of canonical variables describing the bodies only. The field is eliminated by solving inhomogeneous wave equations, applying transverse-traceless projections, and using the Routh functional. By including all special relativistic effects our Hamiltonian extends the results described in classical textbooks of theoretical physics. As an application, the scattering of relativistic objects is considered.     

Basic Aspect of Relativistic Rotation: Franklin Rotation of a Sphere

We give a relativistic treatment to the dynamics of spherical bodies rotating at very high speed. It is found that most of the mass of a homogeneous spherical quark with Franklin rotation is due to the relativistic increase of the mass.     

Rigid Body Motion in Special Relativity

We study the acceleration and collisions of rigid bodies in special relativity. After a brief historical review, we give a physical definition of the term ‘rigid body’ in relativistic straight line motion. We show that the definition of ‘rigid body’ in relativity differs from the usual classical definition, so there is no difficulty in dealing with rigid bodies in relativistic motion. We then describe

1. The motion of a rigid body undergoing constant acceleration to a given velocity.
2. The acceleration of a rigid body due to an applied impulse.
3. Collisions between rigid bodies.

     

The operation of the relativistic Doppler effect

It is shown that the mode of operation of the relativistic Doppler effect and hence also its general formula can be deduced directly from the assumption of a cosmological fundamental reference frame, whose existence is now strongly supported by astronomical observation. Such a frame implies the existence of (relativistic) anisotropy effects on bodies and observers moving relative to it. The Doppler effect consequence is an interesting example of the emergence of relativistic effects from a simple intelligible assumption about light propagation, and shows how this assumption can provide a richer and clearer interpretation of special relativity than does the conventional formal approach.     

Symmetries of space-time,conservation laws and forbidden motion i: General discussion

The classical (first integral) methods of studying restrictions on the possible motion of gravitationally interacting bodies are reviewed. The simple and flexible inequality method is extended to a similar approach to the relationship between possible forbidden motion and (asymptotic) symmetries in the relativistic few-body problem. This extended method is used to reproduce the standard results of bounded motion for a test particle in a Schwarzschild geometry. The existence of bounded motion is shown for the general relativistic few-body problem and the difficulties in determining such bounded motion is analysed. The use of this approach to obtaining a relativistic alternative to the classical Roche lobe analysis in contact binaries is discussed.     

Die Strahlungs-Temperatur bewegter Körper

The Radiation Temperature of Moving Bodies The comparison of the temperatures of two bodies which are in a relative motion is possible by the black-body-radiation of these bodies, unambiguously. Then, Planck's transformation law for the temperature is resulting by Einstein's theory of the transversal Doppler-effect and the aberration and by the laws of heat radiation without additional hypotheses. - Our argument is based on the transformation formulas of the specific radiation intensities which are proved by M. v. Laue (1943) in his relativistic deduction of Wien's law.     

Black holes and Newtonian physics

It is argued that one-way passage is inconsistent with Newtonian physics and thus the dark bodies as thought of by Michell and Laplace cannot be considered as exact analogues of relativistic black holes.     

Relativistic Hall effect

We consider the relativistic deformation of quantum waves and mechanical bodies carrying intrinsic angular momentum (AM). When observed in a moving reference frame, the centroid of the object undergoes an AM-dependent transverse shift. This is the relativistic analogue of the spin-Hall effect, which occurs in free space without any external fields. Remarkably, the shifts of the geometric and energy centroids differ by a factor of 2, and both centroids are crucial for the Lorentz transformations of the AM tensor. We examine manifestations of the relativistic Hall effect in quantum vortices and mechanical flywheels and also discuss various fundamental aspects of this phenomenon. The perfect agreement of quantum and relativistic approaches allows applications at strikingly different scales, from elementary spinning particles, through classical light, to rotating black holes.     

About a physical nature of inertia and its relation to gravitation. II

A physical nature of inertia and its relation to gravitation are discussed. It is proved that the inertia forces have the induction nature and are induced by a special field generated by all moving bodies of the Universe. The relativistic theory of inertia is suggested. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 19–24, October, 2006.     

Transverse waves in a relativistic rigid body

We present relativistic elasticity as a scalar field theory. We apply it to rigid bodies, i.e., relativistic bodies with a nonlinear elastic law and a definite longitudinal wave velocity _l equal to the light velocity,c. We obtain the transverse wave equation with a definite velocity _t , and the relation between _l , _t , and the Poisson coefficient is the classical one. This is an indication that we have the relativistic extension of a classical Hooke elastic law.     

Analytical mechanics in noninertial reference frames

The fundamental equations of the relativistic analytical mechanics of N gravitating bodies in noninertial reference frames are obtained with the application of the apparatus of three-dimensional tensor analysis.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 34–39, September, 1981.     

Boundary-value problem for minimum surface in the three-dimensional Minkowski world

A system of two relativistic equations is derived to describe the plane motion of two identical bodies with a linear interaction potential. The boundary-value problem for the minimum surface in the Minkowski world leads to this system. The nonrelativistic limit is considered.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 91–93, July, 1981.     

Circular relativistic motion of two identical bodies

The circular relativistic motion of two bodies is discussed as the solution of previously obtained equations with a deviating argument in which the deviation of the argument itself is an unknown function of the time. In the case of circular motion the deviation of the argument does not depend on the time and is a root of a transcendental equation derived in the article.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 46–51, December, 1983.     

Extraordinary Electromagnetic Waves in Weakly Relativistic Degenerate Spin-1/2 Magnetized Quantum Plasmas

By using the relativistic quantum magnetohydrodynamic model, the extraordinary electromagnetic waves in magnetized quantum plasmas are investigated with the effects of particle dispersion associated with the quantum Bohm potential effects, the electron spin-1/2 effects, and the relativistic degenerate pressure effects. The electrons are treated as a quantum and magnetized species, while the ions are classical ones. The new general dispersion relations are derived and analyzed in some interesting special cases. Quantum effects are shown to affect the dispersion relations of the extraordinary electromagnetic waves. It is also shown that the relativistic degenerate pressure effects significantly modify the dispersive properties of the extraordinary electromagnetic waves. The present investigation should be useful for understanding the collective interactions in dense astrophysical bodies,such as the atmosphere of neutron stars and the interior of massive white dwarfs.     

Slowly rotating body in the scalar-tensor theory of gravitation

The problem of slow rotation of relativistic bodies in the scalar-tensor theory of gravitation is solved. An equation describing the rotation, its external solution, and the expression for the angular momentum and moment of inertia are obtained in first order with respect to the angular velocity.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 22–26, May, 1981.In conclusion, the author is deeply grateful to V. A. Filimonov for valuable suggestions and remarks.     

The definition of multipole moments for extended bodies

There is considerable freedom in the definition of multipole moments of the energy-momentum tensor of an extended body in general relativity. By studying the corresponding Newtonian theory we obtain guidelines which enable us to choose the most suitable definitions in the relativistic theory. In this way we find two sets, the complete moments and the reduced moments, of which the latter are the most natural choice for studying the dynamics of extended bodies. Expressions as explicit integrals are give for both sets, and the multipole equations of motion of the body are given in a form exact to all orders. Proofs of the relativistic results will appear elsewhere. Presented at the International Conference on Gravitation and Relativity, Copenhagen, July 1971.     

On the screening of the leptonic charge of a body by a condensate of charged bosons

The hypothesis of leptonic charge raises the problem of its neutralization, which is crucial for the stability of material bodies. The screening of the leptonic charge by a charged bosonic condensate is considered. The screening length and the structure of the skin layer are investigated in both the nonrelativistic and relativistic regimes. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 1, 15–20 (10 July 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Tidal accelerations in general relativity

We derive the kinematical magnification of tidal accelerations which occurs for test bodies in highly relativistic orbits preferentially aligned with respect to repeated principal null rays of algebraically special spacetimes. Some examples of astrophysical importance are discussed. A general expression for computing tidal accelerations in the Newman-Penrose formalism is given.