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-affine 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, Plebanski), linear ones, including the Abelian axion (Ni), and find a method for deriving the metric from linear electrodynamics (Toupin, Schoenberg). Finally, we discuss possible non-minimal coupling schemes.Comment: Latex2e, 26 pages. Contribution to "Testing Relativistic Gravity in Space: Gyroscopes, Clocks, Interferometers ...", Proceedings of the 220th Heraeus-Seminar, 22 - 27 August 1999 in Bad Honnef, C. Laemmerzahl et al. (eds.). Springer, Berlin (2000) to be published (Revised version uses Springer Latex macros; Sec. 6 substantially rewritten; appendices removed; the list of references updated

Resolution of dark matter problem in f(T) gravity

In this paper, we attempt to resolve the dark matter problem in f(T) gravity. Specifically, from our model we successfully obtain the flat rotation curves of galaxies containing dark matter. Further, we obtain the density profile of dark matter in galaxies. Comparison of our analytical results shows that our torsion-based toy model for dark matter is in good agreement with empirical data-based models. It shows that we can address the dark matter as an effect of torsion of the space.Comment: 14 pages, 3 figure

A settlement site of the golden horde period in the area of ulan-khol village in the lagansky district of the republic of Kalmykia

© 2020 Academy of Sciences of Tatarstan, A.Kh. Khalikov Archaeology Institute. All rights reserved. The paper discusses a visually identified archaeological site of the Golden Horde period located in an understudied area of the Republic of Kalmykia. The surface finds are represented by fragments of brick ornamented with ceramics, a spindle, copper coins, lead items with direct counterparts in the Golden Horde antiquities of the Lower Volga, Northern Caucasus, Byzantium, and other regions. Brick and slag of melted brick, traces of metal processing in the form of lead splashes and copper smelting waste indicate the presence of craft production in the settlement. The presence of ceramics from the Lower Volga region, North Caucasus and the territory of the Trebizond Empire at the site allows the authors to assume that this was a small settlement possibly located on a caravan route from Majar to Hajji Tarkhan and further to Sarai. In this case, the archaeological site can be interpreted as a caravanserai. The settlement should be studied across wider areas using modern technologies and excavation methods