Fluid-magnetic helicity in axisymmetric stationary relativistic magnetohydrodynamics

The present work is intended to gain a fruitful insight into the understanding of the formations of magneto-vortex configurations and their role in the physical processes of mutual exchange of energies associated with fluid’s motion and the magnetic fields in an axisymmetric stationary hydromagnetic system subject to strong gravitational field (e.g., neutron star/magnetar). It is found that the vorticity flux vector field associated with vorticity 2-form is a linear combination of fluid’s vorticity vector and of magnetic vorticity vector. The vorticity flux vector obeys Helmholtz’s flux conservation. The energy equation associated with the vorticity flux vector field is deduced. It is shown that the mechanical rotation of vorticity flux surfaces contributes to the formation of vorticity flux vector field. The dynamo action for the generation of toroidal components of vorticity flux vector field is described in the presence of meridional circulations. It is shown that the stretching of twisting magnetic lines due to differential rotation leads to the breakdown of gravitational isorotation in the absence of meridional circulations. An explicit expression consists of rotation of vorticity flux surface, energy and angular momentum per baryon for the fluid-magnetic helicity current vector is obtained. The conservation of fluid-magnetic helicity is demonstrated. It is found that the fluid-magnetic helicity displays the energy spectrum arising due to the interaction between the mechanical rotation of vorticity flux surfaces and the fluid’s motion obeying Euler’s equations. The dissipation of a linear combination of modified fluid helicity and magnetic twist is shown to occur due to coupled effect of frame dragging and meridional circulation. It is found that the growing twist of magnetic lines causes the dissipation of modified fluid helicity in the absence of meridional circulations.     

Structure and evolution of shock waves in relativistic magnetohydrodynamics

We derive the existence conditions for relativistic shock waves propagating in a perfectly conducting fluid with a general equation of state that guarantees that the stationary wave has a continuous profile in the presence of weak viscosity. To this end we study the one-dimensional solutions of the magnetohydrodynamic equations with a relativistic viscosity tensor. We allow for anomalous regions of thermodynamic variables and do not use the well-known condition for the convexity of Poisson adiabats. The results lead to relationships among the velocities of magnetoacoustic, Alfvén, and shock waves in front of and behind the discontinuity that prove to be more stringent than the corollaries of the evolution conditions. In the nonrelativistic case and in parallel and perpendicular shock waves, any difference between the two conditions disappears. Zh. éksp. Teor. Fiz. 114, 881–891 (September 1998)     

Center of mass and far field metric in relativistic magnetohydrodynamics

The uniform motion of the center of mass of a charged, conducting fluid, in the presence of an electromagnetic field, is derived in the first post-Newtonian approximation of general relativity. Also the source's far field metric tensor is determined, and it is expressed in terms of parameters known as three-dimensional volume integrals over its interior. These results for the above system permit the physical identification, to post-Newtonian accuracy, of the integration constants and the coordinate systems involved in the Schwarzschild and the Kerr metric tensors.     

Identical motion in relativistic quantum and classical mechanics

The Klein-Gordon equation for the stationary state of a charged particle in a spherically symmetric scalar field is partitioned into a continuity equation and an equation similar to the Hamilton-Jacobi equation. There exists a class of potentials for which the Hamilton-Jacobi equation is exactly obtained and examples of these potentials are given. The partitionAnsatz is then applied to the Dirac equation, where an exact partition into a continuity equation and a Hamilton-Jacobi equation is obtained.     

The relativistic problem of motion in co-moving co-ordinates

The role of co-moving atlases is discussed in connection with a possible formulation of the problem of motion in General Relativity. The concept of co-moving scheme is defined and applied to various cases of physical interest. In particular in the Einstein-Maxwell case, we derive a general uniqueness proof for the Maxwell equations. The dynamical meaning of the equationT _j ^ij =0 is proved, and a scheme for the solution of the problem of motion in co-moving co-ordinates is proposed.     

Notes on relativistic equations of spin motion

Grounds and applications of Bargmann-Michel-Telegdi equations for the precession of the polarization vector of relativistic particles are considered. A critical question in the discussion is the orientation of the rest frame reference vectors. Møller reference frames which keep constant the mutual orientation of the two infinitely close in time rest frames are shown to have a special role. The generally covariant form of the equations is discussed. The assertion that the principle of relativity is violated in the phenomenon of spin precession is proved to be untrue.     

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.     

Generally relativistic time derivatives and equations of motion

Three types of time derivatives of spatial geometrical quantities are considered in the framework of the general theory of relativity. The form of equations of motion (of spin precession and a geodesic) and their physical interpretation are determined by the type of time derivative that is employed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 117–121, January, 1992.     

Equations of motion for a relativistic wave packet

The time derivative of the position of a relativistic wave packet is evaluated. It is found that it is equal to the mean value of the momentum of the wave packet divided by the mass of the particle. The equation derived represents a relativistic version of the second Ehrenfest theorem.     

Effects of bag surface motion with relativistic kinematics

Radial surface motion of the baryon bag is carried out in a model with relativistic kinematics, with confinement the result of volume energy and surface tension and the pion field coupled to the bag surface. We calculate radial wave functions for the nucleon, the Δ(1233) and the Roper resonance N^*(1450), which is identified as the first radial excitation of the nucleon.

Results are used to calculate form factors and pionic decay widths of the baryons examined. The approximations made in these calculations are discussed in extensio.     

An adjustable law of motion for relativistic spherical shells

A classical and a relativistic law of motion for an advancing shell are deduced applying the thin layer approximation. A new parameter connected with the quantity of absorbed matter in the expansion is introduced; this allows the matching of theory with observation.     

Quantum quantifiers of Raman photon pairs with relativistic motion

In this paper, we develop a model for four-level double Raman pairs by exploiting the required optimal conditions for this system that are feasible with real experimental realization. We investigate qualitatively the entanglement, statistical properties, and geometric phase for the pair of Stokes and anti-Stokes photons in the presence of the relativistic motion. We show that these quantifiers are very sensitive to the change of the Rabi frequency under relativistic motion, exhibiting substantial phenomena that depend on this kind of the coupling between the atom and photons. Finally, we explore the relationship between the quantum quantifiers for constant and time-dependent coupling.     

Center-of-mass motion of a system of relativistic Dirac particles

The relativistic center-of-mass motion for a system ofN fermions can be exactly separated because of the linearity of the Dirac operators in momenta which is not possible for quadratic Klein-Gordon particles. The covariant equations derived from Maxwell-Dirac field theory are considered. The center-of-mass equation is still a 4 ^N -component spinor equation. We solve these equations for two- and three-body systems, as well as the relative motion for the non-interacting case, and discuss the quantum numbers and identification of eigenstates and eigenvalues. The results apply for both bound and scattering states. Dedicated to the Third Centenary of the Publication of Principia: Corollary IV.... and therefore the common center of gravity of all bodies acting upon each other (excluding external actions and impediments) is either at rest, or moves uniformly in a right line. Is. Newton, Philosophiae Naturalis Principia Mathematica (S. Pepys, Julii 5, 1686, Londini)     

Equations of motion of a spinning relativistic particle in external fields

We consider the motion of a spinning relativistic particle in external electromagnetic and gravitational fields to first order in the external field but to arbitrary order in the spin. The influence of the spin on the particle trajectory is properly accounted for by describing the spin noncovariantly. Specific calculations are performed through second order in the spin. A simple derivation is presented for the gravitational spin-orbit and spin-spin interactions of a relativistic particle. We discuss the gravimagnetic moment (GM), a particular spin effect in general relativity. We show that for a Kerr black hole the gravimagnetic ratio, i.e., the coefficient of the GM, equals unity (just as the gyromagnetic ratio equals 2 for a charged Kerr hole). The equations of motion obtained for a spinning relativistic particle in an external gravitational field differ substantially from the Papapetrou equations. Zh. éksp. Teor. Fiz. 113, 1537–1557 (May 1998)     

Radiation from relativistic particles in nongeodesic motion in a strong gravitational field

The scalar and electromagnetic radiation emitted by relativistic particles moving along the stable nongeodesic trajectories in the Kerr gravitational field are described. Two particular models of the nongeodesic motion are developed involving a slightly charged rotating black hole and a rotating black hole immersed in an external magnetic field.     

Influence of quantum fluctuations on the motion of relativistic protons in crystals

The influence of multiple scattering and quantum fluctuations in the transverse coordinate, momentum, and energy on the channeling of relativistic protons in a silicon crystal have been studied by computer simulation.     

General relativistic coupling of orbital and rotational motion of the planets

A monadic method of specifying frames of reference is used to investigate the coupling between the orbital and rotational motion of the planets. Expressions are obtained for the general relativistic contributions to the precession of the equinoxes, the nutation of the rotation axis, and the seasonal variations of the length of the day.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 11–15, March, 1981.I am grateful to the participants of the Little Gravitational Seminar of the Gravitation Section at the Ministry of Higher Education of the USSR for their interest in the work.     

Interaction of radiation and a relativistic electron in motion in a constant magnetic field

This paper examines the effect of multiple photon emission on the quantum mechanical state of an electron emitting synchrotron radiation and on the intensity of that radiation. Calculations are done with a variant of perturbation theory based on the use of extended coherent states. A general formula is derived for the number of emitted photons, which allows taking into account their mutual interaction. A model problem is used to demonstrate the absence of the infrared catastrophe in the modified perturbation theory. Finally, the electron density matrix is calculated, and the analysis of this matrix makes it possible to conclude that the degree of the electron’s spatial localization increases with the passage of time if the electron is being accelerated. Zh. éksp. Teor. Fiz. 113, 841–864 (March 1998)