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Yakov Itin

Publications and source records attributed to Yakov Itin.

53 records · Page 3Linked to original sources
arXiv2004

Is the Lorentz signature of the metric of spacetime electromagnetic in origin?

We formulate a premetric version of classical electrodynamics in terms of the excitation H and the field strength F. A local, linear, and symmetric spacetime relation between H and F is assumed. It yields, if electric/magnetic reciprocity is postulated, a Lorentzian metric of spacetime thereby excluding Euclidean signature (which is, nevertheless, discussed in some detail). Moreover, we determine the Dufay law (repulsion of like charges and attraction of opposite ones), the Lenz rule (the relative sign in Faraday's law), and the sign of the electromagnetic energy. In this way, we get a systematic understanding of the sign rules and the sign conventions in electrodynamics. The question in the title of the paper is answered affirmatively.

gr-qc↗
arXiv2003

Maxwell's field coupled nonminimally to quadratic torsion: Induced axion field and birefringence of the vacuum

We consider a possible (parity conserving) interaction between the electromagnetic field $F$ and a torsion field $T^α$ of spacetime. For generic elementary torsion, gauge invariant coupling terms of lowest order fall into two classes that are both nonminimal and {\it quadratic} in torsion. These two classes are displayed explicitly. The first class of the type $\sim F T^2$ yields (undesirable) modifications of the Maxwell equations. The second class of the type $\sim F^2 T^2$ doesn't touch the Maxwell equations but rather modifies the constitutive tensor of spacetime. Such a modification can be completely described in the framework of metricfree electrodynamics. We recognize three physical effects generated by the torsion: (i) An axion field that induces an {\em optical activity} into spacetime, (ii) a modification of the light cone structure that yields {\em birefringence} of the vacuum, and (iii) a torsion dependence of the {\em velocity of light.} We study these effects in the background of a Friedmann universe with torsion. {\it File tor17.tex, 02 August 2003}

gr-qc↗
arXiv2003

Noether currents and charges for Maxwell-like Lagrangians

Hilbert-Noether theorem states that a current associated to diffeomorphism invariance of a Lagrangian vanishes on shell modulo a divergence of an arbitrary superpotential. Application of the Noether procedure to physical Lagrangians yields, however, meaningful (and measurable) currents. The well known solution to this ``paradox'' is to involve the variation of the metric tensor. Such procedure, for the field considered on a fixed (flat) background, is sophisticated logically (one need to introduce the variation of a fixed field) and formal. We analyze the Noether procedure for a generic diffeomorphism invariant $p$-form field model. We show that the Noether current of the field considered on a variable background coincides with the current treated in a fixed geometry. Consistent description of the canonical energy-momentum current is possible only if the dynamics of the geometry (gravitation) is taken into account. However, even the ``truncated'' consideration yields the proper expression. We examine the examples of the free $p$-form gauge field theory, the GR in the coframe representation and the metric-free electrodynamics. Although, the variation of a metric tensor is not acceptable in the latter case, the Noether procedure yields the proper result.

math-ph↗
arXiv2002

The Cauchy Relations in Linear Elasticity Theory

In linear elasticity, we decompose the elasticity tensor into two irreducible pieces with 15 and 6 independent components, respectively. The {\it vanishing} of the piece with 6 independent components corresponds to the Cauchy relations. Thus, for the first time, we recognize the group-theoretical underpinning of the Cauchy relations.

cond-mat↗
arXiv2001

Coframe energy-momentum current. Algebraic properties

The coframe (teleparallel) description of gravity is known as a viable alternative to GR. One of advantages of this model is the existence of a conserved energy-momentum current witch is covariant under all symmetries of the three-parameter Lagrangian. In this paper we study the relation between the covector valued current and the energy-momentum tensor. Algebraic properties of the conserved current for different values of parameters are derived. It is shown that the tensor corresponding to the coframe current is traceless and, in contrast to the electromagnetic field, has in general a non vanishing antisymmetric part. The symmetric part is also non zero for all values of the parameters. Consequently, the conserved current involves the energy-momentum as well as the rotational (spin) properties of the field.

gr-qc↗
arXiv2001

Energy-momentum current for coframe gravity

The obstruction for the existence of an energy momentum tensor for the gravitational field is connected with differential-geometric features of the Riemannian manifold. It has not to be valid for alternative geometrical structures. A teleparallel manifold is defined as a parallelizable differentiable 4D-manifold endowed with a class of smooth coframe fields related by global Lorentz, i.e., SO(1,3) transformations. In this article a general free parametric class of teleparallel models is considered. It includes a 1-parameter subclass of viable models with the Schwarzschild coframe solution. A new form of the coframe field equation is derived from the general teleparallel Lagrangian by introducing the notion of a 3-parameter conjugate field strength $\F^a$. The field equation turns out to have a form completely similar to the Maxwell field equation $d*\F^a=\T^a$. By applying the Noether procedure, the source 3-form $\T^a$ is shown to be connected with the diffeomorphism invariance of the Lagrangian. Thus the source $\T^a$ of the coframe field is interpreted as the total conserved energy-momentum current. The energy-momentum tensor for coframe is defined. The total energy-momentum current of a system of a coframe and a material fields is conserved. Thus a redistribution of the energy-momentum current between a material and a coframe (gravity) fields is possible in principle, unlike as in the standard GR. For special values of parameters, when the GR is reinstated, the energy-momentum tensor gives up the invariant sense, i.e., becomes a pseudo-tensor. Thus even a small-parametric change of GR turns it into a well defined Lagrangian theory.

gr-qc↗
arXiv2001

Conserved currents for general teleparallel models

The obstruction for the existence of an energy momentum tensor for the gravitational field is connected with differential-geometric features of the Riemannian manifold. It has not to be valid for alternative geometrical structures. In this article a general 3-parameter class of teleparallel models is considered. The field equation turns out to have a form completely similar to the Maxwell field equation $d*\F^a=\T^a$. By applying the Noether procedure, the source 3-form $\T^a$ is shown to be connected with the diffeomorphism invariance of the Lagrangian. Thus the source of the coframe field is interpreted as the total conserved energy-momentum current of the system. A reduction of the conserved current to the Noether current and the Noether charge for the coframe field is provided. An energy-momentum tensor for the coframe field is defined in a diffeomorphism invariant and a translational covariant way. The total energy-momentum current of a system is conserved. Thus a redistribution of the energy-momentum current between material and coframe (gravity) field is possible in principle, unlike as in GR. The energy-momentum tensor is calculated for various teleparallel models: the pure Yang-Mills type model, the anti-Yang-Mills type model and the generalized teleparallel equivalent of GR. The latter case can serve as a very close alternative to the GR description of gravity.

gr-qc↗
arXiv2001

On the derivation of the equations of motion in theories of gravity

The equations of motion of massive particles in GR are completely determined by the field equation. We utilize the particular form of Einstein's field equation and propose for the $N$-body problem of the equations that are Lorentz invariant a novel algorithm for the derivation of the equations of motion from the field equations. It is: 1. Compute a static, spherically symmetric solution of the field equation. It will be singular at the origin. This will be taken to be the field generated by a single particle. 2. Move the solution on a trajectory $ {ψ(t)}$ and apply the instantaneous Lorentz transformation based on instantaneous velocity $\dotψ(t)$. 3. Take, as first approximation, the field generated by $N$ particles to be the superposition of the fields generated by the single particles. 4. Compute the leading part of the equation. Hopefully, only terms that involves $\ddotψ(t)$ will be dominant. This is the ``inertial'' part. 5. Compute by the quadratic part of the equation. This is the agent of the ``force''. 6. Equate for each singularity, the highest order terms of the singularities that came from the linear part and the quadratic parts, respectively. This is an equation between the inertial part and the force. The algorithm was applied to Einstein equations. The approximate evolution of scalar curvature lends, in turn, to an invariant scalar equation. The algorithm for it did produce Newton's law of gravitation. This is, also, the starting point for the embedding the trajectories in a common field.

gr-qc↗
arXiv2000

The generalized teleparallel structure

It is proposed to describe a teleparallel structure as a combination of a Riemannian and a symplectic structure. The correspondent invariance group is an intersection of the orthogonal and the symplectic groups. For a 4D manifold it turns to be the basic group of the electro-week interaction $U(1)\times SU(2).$

gr-qc↗
arXiv1999

Coframe teleparallel models of gravity. Exact solutions

The superstring and superbrane theories which include gravity as a necessary and fundamental part renew an interest to alternative representations of general relativity as well as the alternative models of gravity. We study the coframe teleparallel theory of gravity with a most general quadratic Lagrangian. The coframe field on a differentiable manifold is a basic dynamical variable. A metric tensor as well as a metric compatible connection is generated by a coframe in a unique manner. The Lagrangian is a general linear combination of Weitzenböck's quadratic invariants with free dimensionless parameters $\r_1,\r_2,\r_3$. Every independent term of the Lagrangian is a global SO(1,3)-invariant 4-form. For a special choice of parameters which confirms with the local SO(1,3) invariance this theory gives an alternative description of Einsteinian gravity - teleparallel equivalent of GR. We prove that the sign of the scalar curvature of a metric generated by a static spherical-symmetric solution depends only on a relation between the free parameters. The scalar curvature vanishes only for a subclass of models with $\r_1=0$. This subclass includes the teleparallel equivalent of GR. We obtain the explicit form of all spherically symmetric static solutions of the ``diagonal'' type to the field equations for an arbitrary choice of free parameters. We prove that the unique asymptotic-flat solution with Newtonian limit is the Schwarzschild solution that holds for a subclass of teleparallel models with $\r_1=0$. Thus the Yang-Mills-type term of the general quadratic coframe Lagrangian should be rejected.

gr-qc↗
arXiv1999

Test compatible metrics and 2-branes

We propose a sufficient condition for a general spherical symmetric static metric to be compatible with classical tests of gravity. A 1-parametric class of such metrics are constructed. The Schwarzschild metric as well as the Yilmaz-Rosen metric are in this class. By computing the scalar curvature we show that the non-Schwarzschild metrics can be interpreted as close 2-branes. All the manifolds endowed the described metrics contain in a class of pseudo-Riemannian manifolds with a scalar curvature of a fixed sign.

gr-qc↗
arXiv1999

Equation of motion in a scalar model of gravity

A scalar model of gravity is considered. We propose Lorentz invariant field equation $\square f = kη_{ab}f_{,a}f_{,b}$. The aim of this model is to get, approximately, Newton's law of gravity. It is shown that $f=-\frac 1k\ln(1-k\frac mr)$ is the unique spherical symmetric static solution of the field equation. $f$ is taken to be the field of a particle at the origin, having the mass $m$. The field of a particle moving with a constant velocity is taken to be the appropriate Lorentz transformation of $f$. The field $F$ of $N$ particles moving on trajectories ${ψ_j(t)}$ is taken to be, to first order, the superposition of the fields of the particles, where the instantaneous Lorentz transformation of the fields pertaining to the $j$-th particle is ${\dotψ_j(t)}$. When this field is inserted to the field equation the outcome is singular at $({ψ_j(t)},t)$. The singular terms of the l.h.s. and of the r.h.s. are both $O(R^{-2})$. The only way to reduce the singularity in the field equation is by postulating Newton's law of force. It is hoped that this model will be generalized to system of equations that are covariant under general diffeomorphism.

gr-qc↗
arXiv1999

A class of quasi-linear equations in coframe gravity

We have shown recently that the gravity field phenomena can be described by a traceless part of the wave-type field equation. This is an essentially non-Einsteinian gravity model. It has an exact spherically-symmetric static solution, that yields to the Yilmaz-Rosen metric. This metric is very close to the Schwarzchild metric. The wave-type field equation can not be derived from a suitable variational principle by free variations, as it was shown by Hehl and his collaborates. In the present work we are seeking for another field equation having the same exact spherically-symmetric static solution. The differential-geometric structure on the manifold endowed with a smooth orthonormal coframe field is described by the scalar objects of anholonomity and its exterior derivative. We construct a list of the first and second order SO(1,3)-covariants (one- and two-indexed quantities) and a quasi-linear field equation with free parameters. We fix a part of the parameters by a condition that the field equation is satisfied by a quasi-conformal coframe with a harmonic conformal function. Thus we obtain a wide class of field equations with a solution that yields the Majumdar-Papapetrou metric and, in particularly, the Yilmaz-Rosen metric, that is viable in the framework of three classical tests.

gr-qc↗
arXiv1999

On a class of invariant coframe operators with application to gravity

Let a differential 4D-manifold with a smooth coframe field be given. Consider the operators on it that are linear in the second order derivatives or quadratic in the first order derivatives of the coframe, both with coefficients that depend on the coframe variables. The paper exhibits the class of operators that are invariant under a general change of coordinates, and, also, invariant under the global SO(1,3)-transformation of the coframe. A general class of field equations is constructed. We display two subclasses in it. The subclass of field equations that are derivable from action principles by free variations and the subclass of field equations for which spherical-symmetric solutions, Minkowskian at infinity exist. Then, for the spherical-symmetric solutions, the resulting metric is computed. Invoking the Geodesic Postulate, we find all the equations that are experimentally (by the 3 classical tests) indistinguishable from Einstein field equations. This family includes, of course, also Einstein equations. Moreover, it is shown, explicitly, how to exhibit it. The basic tool employed in the paper is an invariant formulation reminiscent of Cartan's structural equations. The article sheds light on the possibilities and limitations of the coframe gravity. It may also serve as a general procedure to derive covariant field equations.

gr-qc↗
arXiv1999

On variations in teleparallelism theories

The variation procedure on a teleparallel manifold is studied. The main problem is the non-commutativity of the variation with the Hodge dual map. We establish certain useful formulas for variations and restate the master formula due to Hehl and his collaborates. Our approach is different and sometimes easier for applications. By introducing the technique of the variational matrix we find necessary and sufficient conditions for commutativity (anti-commutativity) of the variation derivative with the Hodge dual operator. A general formula for the variation of the quadratic-type expression is obtained. The described variational technique are used in two viable field theories: the electro-magnetic Lagrangian on a curved manifold and the Rumpf Lagrangian of the translation invariant gravity.

gr-qc↗
arXiv1998

Gravity on a parallelizable manifold. Exact solutions

The wave type field equation $\square \vt^a=\la \vt^a$, where $\vt^a$ is a coframe field on a space-time, was recently proposed to describe the gravity field. This equation has a unique static, spherical-symmetric, asymptotically-flat solution, which leads to the viable Yilmaz-Rosen metric. We show that the wave type field equation is satisfied by the pseudo-conformal frame if the conformal factor is determined by a scalar 3D-harmonic function. This function can be related to the Newtonian potential of classical gravity. So we obtain a direct relation between the non-relativistic gravity and the relativistic model: every classical exact solution leads to a solution of the field equation. With this result we obtain a wide class of exact, static metrics. We show that the theory of Yilmaz relates to the pseudo-conformal sector of our construction. We derive also a unique cosmological (time dependent) solution of the described type.

gr-qc↗