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 $T^\alpha$ 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}Comment: 6 page

Erratum to: An Entropy Functional for Riemann-Cartan Space-Times

We correct the entropy functional constructed in Int. J. Theor. Phys. 51:362 (2012). The 'on-shell' functional one obtains from this correct functional possesses a holographic structure without imposing any constraint on the spin-angular momentum tensor of matter, in contrast to the conclusion made in the above paper.Comment: 15 pages. These are the preprints of the original paper and its erratum published in Int. J. Theor. Phy

Mining metrics for buried treasure

The same but different: That might describe two metrics. On the surface CLASSI may show two metrics are locally equivalent, but buried beneath one may be a wealth of further structure. This was beautifully described in a paper by M.A.H. MacCallum in 1998. Here I will illustrate the effect with two flat metrics -- one describing ordinary Minkowski spacetime and the other describing a three-parameter family of Gal'tsov-Letelier-Tod spacetimes. I will dig out the beautiful hidden classical singularity structure of the latter (a structure first noticed by Tod in 1994) and then show how quantum considerations can illuminate the riches. I will then discuss how quantum structure can help us understand classical singularities and metric parameters in a variety of exact solutions mined from the Exact Solutions book.Comment: 16 pages, no figures, minor grammatical changes, submitted to Proceedings of the Malcolm@60 Conference (London, July 2004

Gravitational field around a screwed superconducting cosmic string in scalar-tensor theories

We obtain the solution that corresponds to a screwed superconducting cosmic string (SSCS) in the framework of a general scalar-tensor theory including torsion. We investigate the metric of the SSCS in Brans-Dicke theory with torsion and analyze the case without torsion. We show that in the case with torsion the space-time background presents other properties different from that in which torsion is absent. When the spin vanish, this torsion is a $\phi$-gradient and then it propagates outside of the string. We investigate the effect of torsion on the gravitational force and on the geodesics of a test-particle moving around the SSCS. The accretion of matter by wakes formation when a SSCS moves with speed $v$ is investigated. We compare our results with those obtained for cosmic strings in the framework of scalar-tensor theory.Comment: 22 pages, LaTeX, presented at the "XXII - Encontro Nacional de Fisica de Particulas e Campos", Sao Lourenco, MG, Brazi

Gravitation, electromagnetism and cosmological constant in purely affine gravity

The Ferraris-Kijowski purely affine Lagrangian for the electromagnetic field, that has the form of the Maxwell Lagrangian with the metric tensor replaced by the symmetrized Ricci tensor, is dynamically equivalent to the metric Einstein-Maxwell Lagrangian, except the zero-field limit, for which the metric tensor is not well-defined. This feature indicates that, for the Ferraris-Kijowski model to be physical, there must exist a background field that depends on the Ricci tensor. The simplest possibility, supported by recent astronomical observations, is the cosmological constant, generated in the purely affine formulation of gravity by the Eddington Lagrangian. In this paper we combine the electromagnetic field and the cosmological constant in the purely affine formulation. We show that the sum of the two affine (Eddington and Ferraris-Kijowski) Lagrangians is dynamically inequivalent to the sum of the analogous ($\Lambda$CDM and Einstein-Maxwell) Lagrangians in the metric-affine/metric formulation. We also show that such a construction is valid, like the affine Einstein-Born-Infeld formulation, only for weak electromagnetic fields, on the order of the magnetic field in outer space of the Solar System. Therefore the purely affine formulation that combines gravity, electromagnetism and cosmological constant cannot be a simple sum of affine terms corresponding separately to these fields. A quite complicated form of the affine equivalent of the metric Einstein-Maxwell-$\Lambda$ Lagrangian suggests that Nature can be described by a simpler affine Lagrangian, leading to modifications of the Einstein-Maxwell-$\Lambda$CDM theory for electromagnetic fields that contribute to the spacetime curvature on the same order as the cosmological constant.Comment: 17 pages, extended and combined with gr-qc/0612193; published versio

Cartan's spiral staircase in physics and, in particular, in the gauge theory of dislocations

In 1922, Cartan introduced in differential geometry, besides the Riemannian curvature, the new concept of torsion. He visualized a homogeneous and isotropic distribution of torsion in three dimensions (3d) by the "helical staircase", which he constructed by starting from a 3d Euclidean space and by defining a new connection via helical motions. We describe this geometric procedure in detail and define the corresponding connection and the torsion. The interdisciplinary nature of this subject is already evident from Cartan's discussion, since he argued - but never proved - that the helical staircase should correspond to a continuum with constant pressure and constant internal torque. We discuss where in physics the helical staircase is realized: (i) In the continuum mechanics of Cosserat media, (ii) in (fairly speculative) 3d theories of gravity, namely a) in 3d Einstein-Cartan gravity - this is Cartan's case of constant pressure and constant intrinsic torque - and b) in 3d Poincare gauge theory with the Mielke-Baekler Lagrangian, and, eventually, (iii) in the gauge field theory of dislocations of Lazar et al., as we prove for the first time by arranging a suitable distribution of screw dislocations. Our main emphasis is on the discussion of dislocation field theory.Comment: 31 pages, 8 figure

Gravitational field around a time-like current-carrying screwed cosmic string in scalar-tensor theories

In this paper we obtain the space-time generated by a time-like current-carrying superconducting screwed cosmic string(TCSCS). This gravitational field is obtained in a modified scalar-tensor theory in the sense that torsion is taken into account. We show that this solution is comptible with a torsion field generated by the scalar field $\phi$. The analysis of gravitational effects of a TCSCS shows up that the torsion effects that appear in the physical frame of Jordan-Fierz can be described in a geometric form given by contorsion term plus a symmetric part which contains the scalar gradient. As an important application of this solution, we consider the linear perturbation method developed by Zel'dovich, investigate the accretion of cold dark matter due to the formation of wakes when a TCSCS moves with speed $v$ and discuss the role played by torsion. Our results are compared with those obtained for cosmic strings in the framework of scalar-tensor theories without taking torsion into account.Comment: 21 pages, no figures, Revised Version, presented at the "XXIV- Encontro Nacional de Fisica de Particulas e Campos ", Caxambu, MG, Brazil, to appear in Phys. Rev.

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

Gradient models of the axion-photon coupling

We establish an extended version of the Einstein - Maxwell - axion model by introducing into the Lagrangian cross-terms, which contain the gradient four-vector of the pseudoscalar (axion) field in convolution with the Maxwell tensor. The gradient model of the axion-photon coupling is applied to cosmology: we analyze the Bianchi-I type Universe with an initial magnetic field, electric field induced by the axion-photon interaction, cosmological constant and dark matter, which is described in terms of the pseudoscalar (axion) field. Analytical, qualitative and numerical results are presented in detail for two distinguished epochs: first, for the early Universe with magnetic field domination; second, for the stage of late-time accelerated expansion.Comment: 26 pages, 5 figures, accepted for publication in The European Physical Journal