arXiv subjects

Yuri N. Obukhov

Publications and source records attributed to Yuri N. Obukhov.

At least 73 records · Page 4Linked to original sources

arXiv2015

Spin-torsion coupling and gravitational moments of Dirac fermions: theory and experimental bounds

We discuss the quantum dynamics of the Dirac fermion particle in a gauge gravitational field. The minimal as well as the Pauli-type nonminimal coupling of a fermion with external fields is studied, bringing into consideration the notions of the translational and the Lorentz gravitational moments. The anomalous gravitomagnetic and gravitoelectric moments are ruled out on the basis of the covariance arguments. We derive the general Foldy-Wouthuysen transformation for an arbitrary configuration of the gauge gravitational field without assuming it weak. Making use of the Foldy-Wouthuysen Hamiltonian for the Dirac particle coupled to magnetic field in a noninertial reference system, we analyze the recent experimental data and obtain bounds on the spacetime torsion.

hep-th↗

arXiv2014

Equations of motion in scalar-tensor theories of gravity: A covariant multipolar approach

We discuss the dynamics of extended test bodies for a large class of scalar-tensor theories of gravitation. A covariant multipolar Mathisson-Papapetrou-Dixon type of approach is used to derive the equations of motion in a systematic way for both Jordan and Einstein formulations of these theories. The results obtained provide the framework to experimentally test scalar-tensor theories by means of extended test bodies.

gr-qc↗

arXiv2014

Equations of motion in metric-affine gravity: A covariant unified framework

We derive the equations of motion of extended deformable bodies in metric-affine gravity. The conservation laws which follow from the invariance of the action under the general coordinate transformations are used as a starting point for the discussion of the dynamics of extended deformable test bodies. By means of a covariant approach, based on Synge's world function, we obtain the master equation of motion for an arbitrary system of coupled conserved currents. This unified framework is then applied to metric-affine gravity. We confirm and extend earlier findings; in particular, we once again demonstrate that it is only possible to detect the post-Riemannian spacetime geometry by ordinary (non-microstructured) test bodies if gravity is nonminimally coupled to matter.

gr-qc↗

arXiv2014

Motion of spinning test bodies in Kerr spacetime

We investigate the motion of spinning test bodies in General Relativity. By means of a multipolar approximation method for extended test bodies we derive the equations of motion, and classify the orbital motion of pole-dipole test bodies in the equatorial plane of the Kerr geometry. An exact expression for the periastron shift of a spinning test body is given. Implications of test body spin corrections are studied and compared with the results obtained by means of other approximation schemes.

gr-qc↗

arXiv2014

Conservation laws in gravity: A unified framework

We study general metric-affine theories of gravity in which the metric and connection are the two independent fundamental variables. In this framework, we use Lagrange-Noether methods to derive the identities and the conservation laws that correspond to the invariance of the action under general coordinate transformations. The results obtained are applied to generalized models with nonminimal coupling of matter and gravity, with a coupling function that depends arbitrarily on the covariant gravitational field variables.

gr-qc↗

arXiv2014

Prospects of detecting spacetime torsion

How to detect spacetime torsion? In this essay we provide the theoretical basis for an answer to this question. Multipolar equations of motion for a very general class of gravitational theories with nonminimal coupling in spacetimes admitting torsion are given. Our findings provide a framework for the systematic testing of whole classes of theories with the help of extended test bodies. One surprising feature of nonminimal theories turns out to be their potential sensitivity to torsion of spacetime even in experiments with ordinary (not microstructured) test matter.

gr-qc↗

arXiv2013

Equations of motion in gravity theories with nonminimal coupling: a loophole to detect torsion macroscopically?

We derive multipolar equations of motion for gravitational theories with general nonminimal coupling in spacetimes admitting torsion. Our very general findings allow for the systematic testing of whole classes of theories by means of extended test bodies. One peculiar feature of certain subclasses of nonminimal theories turns out to be their sensitivity to post-Riemannian spacetime structures even in experiments without microstructured test matter.

gr-qc↗

arXiv2013

Spin Precession in Inertial and Gravitational Fields

We discuss the motion of spin in inertial and gravitational fields. The coupling of spin with rotation and the gravitomagnetic field has already been extensively studied; therefore, we focus here on the inertial and gravitational spin-orbit couplings. In particular, we investigate the classical and quantum aspects of spin precession and spin-orbit coupling in an arbitrary translationally accelerated frame of reference as well as the exterior Schwarzschild spacetime. Moreover, in connection with Einstein's principle of equivalence, we clarify the relation between the inertial and gravitational spin-orbit couplings.

gr-qc↗

arXiv2013

Spin in an arbitrary gravitational field

We study the quantum mechanics of a Dirac fermion on a curved spacetime manifold. The metric of the spacetime is completely arbitrary, allowing for the discussion of all possible inertial and gravitational field configurations. In this framework, we find the Hermitian Dirac Hamiltonian for an arbitrary classical external field (including the gravitational and electromagnetic ones). In order to discuss the physical content of the quantum-mechanical model, we further apply the Foldy-Wouthuysen transformation, and derive the quantum equations of motion for the spin and position operators. We analyse the semiclassical limit of these equations and compare the results with the dynamics of a classical particle with spin in the framework of the standard Mathisson-Papapetrou theory and in the classical canonical theory. The comparison of the quantum mechanical and classical equations of motion of a spinning particle in an arbitrary gravitational field shows their complete agreement.

gr-qc↗

arXiv2013

Unraveling gravity beyond Einstein with extended test bodies

The motion of test bodies in gravity is tightly linked to the conservation laws. This well-known fact in the context of General Relativity is also valid for gravitational theories which go beyond Einstein's theory. Here we derive the equations of motion for test bodies for a very large class of gravitational theories with a general nonminimal coupling to matter. These equations form the basis for future systematic tests of alternative gravity theories. Our treatment is covariant and generalizes the classic Mathisson-Papapetrou-Dixon result for spinning (extended) test bodies. The equations of motion for structureless test bodies turn out to be surprisingly simple, despite the very general nature of the theories considered.

gr-qc↗

arXiv2013

On Poincaré gauge theory of gravity, its equations of motion, and Gravity Probe B

Ever since E.Cartan in the 1920s enriched the geometric framework of general relativity (GR) by introducing a {\it torsion} of spacetime, the question arose whether one could find a measurement technique for detecting the presence of a torsion field. Mao et al.(2007) claimed that the rotating quartz balls in the gyroscopes of the Gravity Probe B experiment, falling freely on an orbit around the Earth, should "feel" the torsion. Similarly, March et al.(2011) argue with the precession of the Moon and the Mercury and extend later their considerations to the Lageos satellite.--- A consistent theory of gravity with torsion emerged during the early 1960's as gauge theory of the Poincaré group. This Poincaré gauge theory of gravity incorporates as simplest viable cases the Einstein-Cartan(-Sciama-Kibble) theory (EC), the teleparallel equivalent GR|| of GR, and GR itself. So far, PG and, in particular, the existence of torsion have {\it not} been experimentally confirmed. However, PG is to be considered as the standard theory of gravity with torsion because of its very convincing gauge structure.--- Since the early 1970s up to today, different groups have shown more or less independently that torsion couples only to the {\it elementary particle spin} and under no circumstances to the orbital angular momentum of test particles. This is established knowledge and we reconfirm this conclusion by discussing the energy-momentum law of PG, which has same form for all versions of PG. Therefore, we conclude that, unfortunately, the investigations of Mao et al. and March et al. do not yield any information on torsion.

gr-qc↗

arXiv2013

Conservation laws in gravitational theories with general nonminimal coupling

We use the Lagrange-Noether methods to derive the conservation laws for models in which matter interacts nonminimally with the gravitational field. The nonminimal coupling function can depend arbitrarily on the gravitational field strength. The obtained result generalizes earlier findings. The generalized conservation laws provide the basis for the derivation of the equations of motion for the nonminimally coupled test bodies.

gr-qc↗

arXiv2013

Covariant equations of motion for test bodies in gravitational theories with general nonminimal coupling

We present a covariant derivation of the equations of motion for test bodies for a wide class of gravitational theories with nonminimal coupling, encompassing a general interaction via the complete set of 9 parity-even curvature invariants. The equations of motion for spinning test bodies in such theories are explicitly derived by means of Synge's expansion technique. Our findings generalize previous results in the literature and allow for a direct comparison to the general relativistic equations of motion of pole-dipole test bodies.

gr-qc↗

arXiv2012

Relativistic Lagrangian model of a nematic liquid crystal interacting with an electromagnetic field

We develop a relativistic variational model for a nematic liquid crystal interacting with an electro- magnetic field. The constitutive relation for a general anisotropic uniaxial diamagnetic and dielectric medium is analyzed. We discuss light wave propagation in this moving uniaxial medium, for which the corresponding optical metrics are identified explicitly. A Lagrangian for the coupled system of a nematic liquid crystal and the electromagnetic field is constructed, from which a complete set of equations of motion for the system is derived. The canonical energy-momentum and spin tensors are systematically obtained. We compare our results with those within the non-relativistic models. As an application of our general formalism, we discuss the so-called Abraham-Minkowski controversy on the momentum of light in a medium.

physics.class-ph↗

arXiv2012

Conservation Laws and Stress-energy-momentum Tensors for Systems with Background Fields

This article attempts to delineate the roles played by non-dynamical background structures and Killing symmetries in the construction of stress-energy-momentum tensors generated from a diffeomorphism invariant action density. An intrinsic coordinate independent approach puts into perspective a number of spurious arguments that have historically lead to the main contenders, viz the Belinfante-Rosenfeld stress-energy-momentum tensor derived from a Noether current and the Einstein-Hilbert stress-energy-momentum tensor derived in the context of Einstein's theory of general relativity. Emphasis is placed on the role played by non-dynamical background (phenomenological) structures that discriminate between properties of these tensors particularly in the context of electrodynamics in media. These tensors are used to construct conservation laws in the presence of Killing Lie-symmetric background fields.

physics.class-ph↗

arXiv2012

Relativistic analysis of the dielectric Einstein box: Abraham, Minkowski and total energy-momentum tensors

We analyse the "Einstein box" thought experiment and the definition of the momentum of light inside matter. We stress the importance of the total energy-momentum tensor of the closed system (electromagnetic field plus material medium) and derive in detail the relativistic expressions for the Abraham and Minkowski momenta, together with the corresponding balance equations for an isotropic and homogeneous medium. We identify some assumptions hidden in the Einstein box argument, which make it weaker than it is usually recognized. In particular, we show that the Abraham momentum is not uniquely selected as the momentum of light in this case.

physics.class-ph↗

arXiv2012

Extended Einstein-Cartan theory a la Diakonov: the field equations

Diakonov formulated a model of a primordial Dirac spinor field interacting gravitationally within the geometric framework of the Poincaré gauge theory (PGT). Thus, the gravitational field variables are the orthonormal coframe (tetrad) and the Lorentz connection. A simple gravitational gauge Lagrangian is the Einstein-Cartan choice proportional to the curvature scalar plus a cosmological term. In Diakonov's model the coframe is eliminated by expressing it in terms of the primordial spinor. We derive the corresponding field equations for the first time. We extend the Diakonov model by additionally eliminating the Lorentz connection, but keeping local Lorentz covariance intact. Then, if we drop the Einstein-Cartan term in the Lagrangian, a nonlinear Heisenberg type spinor equation is recovered in the lowest approximation.

gr-qc↗

arXiv2012

A gauge theoretic approach to elasticity with microrotations

We formulate elasticity theory with microrotations using the framework of gauge theories, which has been developed and successfully applied in various areas of gravitation and cosmology. Following this approach, we demonstrate the existence of particle-like solutions. Mathematically this is due to the fact that our equations of motion are of Sine-Gordon type and thus have soliton type solutions. Similar to Skyrmions and Kinks in classical field theory, we can show explicitly that these solutions have a topological origin.

math-ph↗