Yuri N. Obukhov

Poincare gauge gravity: Selected topics

In the gauge theory of gravity based on the Poincare group (the semidirect product of the Lorentz group and the spacetime translations) the mass (energy–momentum) and the spin are treated on an equal footing as the sources of the gravitational field. The corresponding spacetime manifold carries the Riemann–Cartan geometric structure with the nontrivial curvature and torsion. We describe some aspects of the classical Poincare gauge theory of gravity. Namely, the Lagrange–Noether formalism is presented in full generality, and the family of quadratic (in the curvature and the torsion) models is analyzed in detail. We discuss the special case of the spinless matter and demonstrate that Einsteins theory arises as a degenerate model in the class of the quadratic Poincare theories. Another central point is the overview of the so-called double duality method for constructing of the exact solutions of the classical field equations.

Linear media in classical electrodynamics and the Post constraint

Abstract The Maxwell equations are formulated in a generally covariant and metric-free way in 1 + 3 and subsequently in 4 dimensions. For this purpose, we use the excitations D , H and the field strengths E , B . A local and linear constitutive law between excitations and field strengths is assumed, with a constitutive tensor of 36 components. The properties of this tensor are discussed. In particular, we address the validity of the Post constraint. In this connection, the Tellegen gyrator, the axion field, and the “perfect electromagnetic conductor” of Lindell and Sihvola are compared with each other.

Measuring a piecewise constant axion field in classical electrodynamics

Abstract In order to settle the problem of the “Post constraint” in material media, we consider the propagation of a plane electromagnetic wave in a medium with a piecewise constant axion field. Although a constant axion field does not affect the wave propagation in a homogeneous medium, we show that the reflection and transmission of a wave at an interface between the two media is sensitive to the difference of the axion values. This observation can be used to determine experimentally the axion piece in matter despite the fact that a constant axion value does not contribute to the Maxwell equations.

Electromagnetic energy-momentum and forces in matter

Abstract We discuss the electromagnetic energy–momentum distribution and the mechanical forces of the electromagnetic field in material media. There is a long-standing controversy on these notions. The Minkowski and the Abraham energy–momentum tensors are the most well-known ones. We propose a solution of this problem which appears to be natural and self-consistent from both a theoretical and an experimental point of view.

Relativistic nature of a magnetoelectric modulus of Cr2O3 crystals : A four-dimensional pseudoscalar and its measurement

The magnetoelectric effect of chromium sesquioxide Cr2O3 has been determined experimentally as a function of temperature. One measures the electric field-induced magnetization on Cr2O3 crystals or the magnetic field-induced polarization. From the magnetoelectric moduli of Cr2O3 we extract a four-dimensional relativistic invariant pseudoscalar alpha-tilde. It is temperature dependent and of the order of ~10−4/Z0, with Z0 as vacuum impedance. We show that the new pseudoscalar is odd under parity transformation and odd under time inversion. Moreover, alpha-tilde is for Cr2O3 what Tellegens gyrator is for two port theory, the axion field for axion electrodynamics, and the PEMC (perfect electromagnetic conductor) for electrical engineering.

Spin dynamics in gravitational fields of rotating bodies and the equivalence principle

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.

How Does the Electromagnetic Field Couple to Gravity, in Particular to Metric, Nonmetricity, Torsion, and Curvature?

The coupling of the electromagnetic field to gravity is an age-old problem. Presently, there is a resurgence of interest in it, mainly for two reasons: (i) Experimental investigations are under way with ever increasing precision, be it in the laboratory or by observing outer space. (ii) One desires to test out alternatives to Einstein’s gravitational theory, in particular those of a gauge-theoretical nature, like Einstein-Cartan theory or metric-afine gravity.— A clean discussion requires a reflection on the foundations of electrodynamics. If one bases electrodynamics on the conservation laws of electric charge and magnetic flux, one finds Maxwell’s equations expressed in terms of the excitation H = (D,H) and the field strength F = (E,B) without any intervention of the metric or the linear connection of spacetime. In other words, there is still no coupling to gravity. Only the constitutive law H = functional(F) mediates such a coupling. We discuss the different ways of how metric, nonmetricity, torsion, and curvature can come into play here. Along the way, we touch on non-local laws (Mashhoon), non-linear ones (Born-Infeld, Heisenberg-Euler, Plebaśki), linear ones, including the Abelian axion (Ni), and fid a method for deriving the metric from linear electrodynamics (Toupin, Schonberg). Finally, we discuss possible non-minimal coupling schemes.

Regularizing role of teleparallelism

The properties of the gravitational energy-momentum 3-form and of the superpotential 2-form are discussed in the covariant teleparallel framework, where the Weitzenbock connection represents inertial effects related to the choice of the frame. Because of 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.

Fresnel analysis of wave propagation in nonlinear electrodynamics

We study wave propagation in local nonlinear electrodynamical models. Particular attention is paid to the derivation and the analysis of the Fresnel equation for the wave covectors. For the class of local nonlinear Lagrangian nondispersive models, we demonstrate how the originally quartic Fresnel equation factorizes, yielding the generic birefringence effect. We show that the closure of the effective constitutive (or jump) tensor is necessary and sufficient for the absence of birefringence, i.e., for the existence of a unique light cone structure. As another application of the Fresnel approach, we analyze the light propagation in a moving isotropic nonlinear medium. The corresponding effective constitutive tensor contains nontrivial skewon and axion pieces. For nonmagnetic matter, we find that birefringence is induced by the nonlinearity, and derive the corresponding optical metrics.

Wave propagation in linear electrodynamics

The Fresnel equation governing the propagation of electromagnetic waves for the most general linear constitutive law is derived. The wave normals an found to lie, in general, on a fourth order surface. When the constitutive coefficients satisfy the so-called reciprocity or closure relation, one can define a duality operator on the space of the two-forms. We prove that the closure relation is a sufficient condition for the reduction of the fourth order surface to the familiar second order light cone structure. We finally study whether this condition is also necessary.