arXiv subjects

Y. Itin

Publications and source records attributed to Y. Itin.

2 recordsLinked to original sources

arXiv2008

Backwards on Minkowski's road. From 4D to 3D Maxwellian electromagnetism

Minkowski's concept of a four-dimensional physical space is a central paradigm of modern physics. The three-dimensional Maxwellian electrodynamics is uniquely generalized to the covariant four-dimensional form. Is the (1+3) decomposition of the covariant four-dimensional form unique? How do the different sign assumptions of electrodynamics emerge from this decomposition? Which of these assumptions are fundamental and which of them may be modified? How does the Minkowski space-time metric emerge from this preliminary metric-free construction? In this paper we are looking for answers to the problems mentioned. Our main result is the derivation of four different possible sets of electrodynamic equations which may occur in different types of isotropic electromagnetic media. The wave propagation in each of these media is described by the Minkowskian optical metrics. Moreover, the electric and magnetic energies are nonnegative in all cases. We also show that the correct directions of the Lorentz force (as a consequence of the Dufay and the Lenz rules) hold true for all these cases. However, the differences between these four types of media must have a physical meaning. In particular, the signs of the three electromagnetic invariants are different.

gr-qc↗

arXiv1997

Gravity on parallelizable manifold

General relativity postulates that the gravity field is defined on a Riemannian manifold. The field equations are $R^μ_ν= 0$ i.e. Ricci's curvature tensor vanishes. The field equations have to be augmented by natural physical requirements like orientability, time orientability and existence of a spinorial structure. Moreover, it is impossible to define the energy of the gravity field only by the metric tensor. We suggest to impose an additional structure and consider parallelizable manifold i.e. manifolds for which a smooth field of frames exists. The derivation of the field equations is by an action principle. A Lagrangian, which is quadratic in the differentials, is defined. The minimum of the action is achieved at a $16 \times 16$ second order quasi linear system. It is of Laplacian type. The system admits a unique exact solution for a centrally symmetric, static and assimptotically flat field. The resulting metric is the celebrated Rosen metric, which is very close to the Schwarzchild metric. The two are intrinsicly different since the scalar curvature of the Schuarzschild metric is zero, in contrast to Rosen's which is positive. The suggested field admits black holes which are briefly discussed.

gr-qc↗