arXiv subjects
Publications and source records attributed to Yuri N. Obukhov.
We report on the multipolar equations of motion for spinning test bodies in the de Sitter spacetime of constant positive curvature. The dynamics of spinning particles is discussed for the two supplementary conditions of Frenkel and Tulczyjew. Furthermore, the 4-momentum and the spin are explicitly expressed in terms of the spacetime coordinates with the help of the 10 Killing vectors available in de Sitter spacetime.
We discuss the dynamics of the Dirac fermions in the general strong gravitational and electromagnetic fields. We derive the general Hermitian Dirac Hamiltonian and transform it to the Foldy-Wouthuysen representation for the spatially isotropic metric. The quantum operator equations of motion are obtained and the semiclassical limit is analyzed. The comparison of the quantum mechanical and classical equations shows their complete agreement. The helicity dynamics in strong fields is discussed. Squaring the covariant Dirac equation explicitly shows a similarity of the interactions of electromagnetic and gravitational fields with a charged and spinning particle.
We study the motion of spinning test bodies in the de Sitter spacetime of constant positive curvature. With the help of the 10 Killing vectors, we derive the 4-momentum and the tensor of spin explicitly in terms of the spacetime coordinates. However, in order to find the actual trajectories, one needs to impose the so-called supplementary condition. We discuss the dynamics of spinning test bodies for the cases of the Frenkel and Tulczyjew conditions.
The complete explicitly covariant 4-dimensional description of the dynamics of a free classical particle with spin within the framework of the special relativity theory is presented. The key point of our approach is the the introduction of the new vector field which enables to define the analogues of the mean spin and position variables. The supplementary conditions are discussed and it is demonstrated that the Frenkel condition unambiguously determines the dynamics of a spinning particle.
Da Rocha and Rodigues (RR) claim (i) that in classical electrodynamics in vector calculus the distinction between polar and axial vectors and in exterior calculus between twisted and untwisted forms is inappropriate and superfluous, and (ii) that they can derive the Lorentz force equation from Maxwell's equations. As to (i), we point out that the distinction of polar/axial and twisted/untwisted derives from the property of the electric charge of being a pure scalar, that is, not carrying any screw sense. Therefore, the mentioned distinctions are necessary ingredients in any fundamental theory of electrodynamics. If one restricted the allowed coordinate transformations to those with positive Jacobian determinants (or prescribed an equivalent constraint), then the RR scheme could be accommodated; however, such a restriction is illegal since electrodynamics is, in fact, also covariant under transformations with negative Jacobians. As to (ii), the "derivation" of the Lorentz force from Maxwell's equations, we point out that RR forgot to give the symbol F (the field strength) in Maxwell's equations an operational meaning in the first place. Thus, their proof is empty. Summing up: the approach of RR does not bring in any new insight into the structure of electrodynamics.
The energy and momentum transported by exact plane gravitational-wave solutions of Einstein equations are computed using the teleparallel equivalent formulation of Einstein's theory. It is shown that these waves transport neither energy nor momentum. A comparison with the usual linear plane gravitational-waves solution of the linearized Einstein equation is presented.
The properties of the gravitational energy-momentum 3-form and of the superpotential 2-form are discussed in the covariant teleparallel framework, where the Weitzenböck connection represents inertial effects related to the choice of the frame. Due to its odd asymptotic behavior, the contribution of the inertial effects often yields unphysical (divergent or trivial) results for the total energy of the system. However, in the covariant teleparallel approach, the energy is always finite and nontrivial. The teleparallel connection plays a role of a regularizing tool which subtracts the inertial effects without distorting the true gravitational contribution. As a crucial test of the covariant formalism, we reanalyze the computation of the total energy of the Schwarzschild and the Kerr solutions.
We discuss the quantum and classical dynamics of a particle with spin in the gravitational field of a rotating source. A relativistic equation describing the motion of classical spin in curved spacetimes is obtained. We demonstrate that the precession of the classical spin is in a perfect agreement with the motion of the quantum spin derived from the Foldy-Wouthuysen approach for the Dirac particle in a curved spacetime. We show that the precession effect depends crucially on the choice of a tetrad. The results obtained are compared to the earlier computations for different tetrad gauges.
We discuss the possibility to perform and use the exact Foldy-Wouthuysen transformation (EFWT) for the Dirac spinor coupled to different CPT and Lorentz violating terms. The classification of such terms is performed, selecting those of them which admit EFWT. For the particular example of an axial vector field, which can be associated with the completely antisymmetric torsion, we construct an explicit EFWT in the case when only a timelike component of this axial vector is present. In the cases when EFWT is not possible, one can still use the corresponding technique for deriving the perturbative Foldy-Wouthuysen transformation, as is illustrated in a particular example in the Appendix.
The equations of motion for matter in non-Riemannian spacetimes are derived via a multipole method. It is found that only test bodies with microstructure couple to the non-Riemannian spacetime geometry. Consequently it is impossible to detect spacetime torsion with the satellite experiment Gravity Probe B, contrary to some recent claims in the literature.
We derive the equations of motion in metric-affine gravity by making use of the conservation laws obtained from Noether's theorem. The results are given in the form of propagation equations for the multipole decomposition of the matter sources in metric-affine gravity, i.e., the canonical energy-momentum current and the hypermomentum current. In particular, the propagation equations allow for a derivation of the equations of motion of test particles in this generalized gravity theory, and allow for direct identification of the couplings between the matter currents and the gauge gravitational field strengths of the theory, namely, the curvature, the torsion, and the nonmetricity. We demonstrate that the possible non-Riemannian spacetime geometry can only be detected with the help of the test bodies that are formed of matter with microstructure. Ordinary gravitating matter, i.e., matter without microscopic internal degrees of freedom, can probe only the Riemannian spacetime geometry. Thereby, we generalize previous results of general relativity and Poincare gauge theory.
Relativity theory is useful for understanding the phenomenology of the magnetoelectric effect of the antiferromagnet chromium sesquioxide Cr_2 O_3 in two respects: (i) One gets a clear idea about the physical dimensions of the electromagnetic quantities involved, in particular about the dimensions of the magnetoelectric moduli that we suggest to tabulate in future as dimensionless relative quantities; (ii) one can recognize and extract a temperature dependent, 4-dimensional pseudoscalar from the data of magnetoelectric experiments with Cr_2 O_3. This pseudoscalar piece of Cr_2 O_3 is odd under time reflections and parity transformations and is structurally related ("isomorphic") to the gyrator of electric network theory, the axion of particle physics, and the perfect electromagnetic conductor of electrical engineering.
We derive the equations of motion of test bodies for a theory with nonminimal coupling by means of a multipole method. The propagation equations for pole-dipole particles are worked out for a gravity theory with a very general coupling between the curvature scalar and the matter fields. Our results allow for a systematic comparison with the equations of motion of general relativity and other gravity theories.
We start from a local and linear spacetime relation between the electromagnetic excitation and the field strength. Then we study the generally covariant Fresnel surfaces for light rays and light waves. The metric and the connection of spacetime are left unspecified. Accordingly, our framework is ideally suited for a search of possible violations of the Lorentz symmetry in the photon sector of the extended standard model. We discuss how the skewon part of the constitutive tensor, if suitably parametrized, influences the Fresnel surfaces and disturbs the light cones of vacuum electrodynamics. Conditions are specified that yield the reduction of the original quartic Fresnel surface to the double light cone structure (birefringence) and to the single light cone. Qualitatively, the effects of the real skewon field can be compared to those in absorbing material media. In contrast, the imaginary skewon field can be interpreted in terms of non-absorbing media with natural optical activity and Faraday effects. The astrophysical data on gamma-ray bursts are used for deriving an upper limit for the magnitude of the skewon field.
The problem of the electromagnetic energy-momentum tensor is among the oldest and the most controversial in macroscopic electrodynamics. In the center of the issue is a dispute about the Minkowski and the Abraham tensors for moving media. An overview of the current situation is presented. After putting the discussion into a general Lagrange-Noether framework, the Minkowski tensor is recovered as a canonical energy-momentum. It is shown that the balance equations of energy, momentum, and angular momentum are always satisfied for an open electromagnetic system despite the lack of the symmetry of the canonical tensor. On the other hand, although the Abraham tensor is not defined from first principles, one can formulate a general symmetrization prescription provided a timelike vector is available. We analyze in detail the variational model of a relativistic ideal fluid with isotropic electric and magnetic properties interacting with the electromagnetic field. The relation between the Minkowski energy-momentum tensor, the canonical energy-momentum of the medium and the Abraham tensor is clarified. It is demonstrated that the Abraham energy-momentum is relevant when the 4-velocity of matter is the only covariant variable that enters the constitutive tensor.
We develop a general approach, based on the Lagrange-Noether machinery, to the definition of invariant conserved currents for gravity theories with general coordinate and local Lorentz symmetries. In this framework, every vector field ξon spacetime generates, in any dimension n, for any Lagrangian of gravitational plus matter fields and for any (minimal or nonminimal) type of interaction, a current J[ξ] with the following properties: (1) the current (n-1)-form J[ξ] is constructed from the Lagrangian and the generalized field momenta, (2) it is conserved, d J[ξ] = 0, when the field equations are satisfied, (3) J[ξ]= dΠ[ξ] "on shell", (4) the current J[ξ], the superpotential Π[ξ], and the charge Q[ξ] = \int J[ξ] are invariant under diffeomorphisms and the local Lorentz group. We present a compact derivation of the Noether currents associated with diffeomorphisms and apply the general method to compute the total energy and angular momentum of exact solutions in several physically interesting gravitational models.
Previously, we have developed a general method to construct invariant conserved currents and charges in gravitational theories with Lagrangians that are invariant under spacetime diffeomorphisms and local Lorentz transformations. This approach is now generalized to the case when the local Lorentz group is replaced by an arbitrary local gauge group. The particular examples include the Maxwell and Yang-Mills fields coupled to gravity with Abelian and non-Abelian local internal symmetries, and the metric-affine gravity in which the local Lorentz spacetime group is extended to the local general linear group.
We review the application of torsion in field theory. First we show how the notion of torsion emerges in differential geometry. In the context of a Cartan circuit, torsion is related to translations similar as curvature to rotations. Cartan's investigations started by analyzing Einsteins general relativity theory and by taking recourse to the theory of Cosserat continua. In these continua, the points of which carry independent translational and rotational degrees of freedom, there occur, besides ordinary (force) stresses, additionally spin moment stresses. In a 3-dimensional continuized crystal with dislocation lines, a linear connection can be introduced that takes the crystal lattice structure as a basis for parallelism. Such a continuum has similar properties as a Cosserat continuum, and the dislocation density is equal to the torsion of this connection. Subsequently, these ideas are applied to 4-dimensional spacetime. A translational gauge theory of gravity is displayed (in a Weitzenboeck or teleparallel spacetime) as well as the viable Einstein-Cartan theory (in a Riemann-Cartan spacetime). In both theories, the notion of torsion is contained in an essential way. Cartan's spiral staircase is described as a 3-dimensional Euclidean model for a space with torsion, and eventually some controversial points are discussed regarding the meaning of torsion.