Magnetic field reversals and topological entropy in non-geodesic hyperbolic dynamos

Earlier, Chicone, Latushkin and Montgomery-Smith [Comm Math Phys (1997)] have proved the existence of a fast dynamo operator, in compact two-dimensional manifold, as long as its Riemannian curvature be constant and negative. More recently Gallet and Petrelis [Phys Rev \textbf{E}, 80 (2009)] have investigated saddle-node bifurcation, in turbulent dynamos as modelling for magnetic field reversals. Since saddle nodes are created in hyperbolic flows, this provides us with physical motivation to investigate these reversals in a simple kinematic dynamo model obtained from a force-free non-geodesic steady flow in Lobachevsky plane. Magnetic vector potential grows in one direction and decays in the other under diffusion. Magnetic field differential 2-form is orthogonal to the plane. A restoring forcing dynamo in hyperbolic space is also given. Magnetic field reversals are obtained from this model. Topological entropies [Klapper and Young, Comm Math Phys (1995)] are also computed

Cosmological magnetic helicity and birefrigence from primordial torsion in Lorentz violation theories

Cosmological magnetic helicity has been thought to be a fundamental agent for magnetic field amplification in the universe. More recently Semikoz and Sokoloff [Phys Rev Lett 92 (2004): 131.301.] showed that the weakness of the seed fields did not necessarily imply the weakness of magnetic cosmological helicity. In this paper we present a derivation of dynamo equation based upon the flat torsion photon non-minimal coupling through Riemann-Cartan spacetime. From this derivation one computes the necessary conditions for a flat torsion field to generate a galactic dynamo seed, from the cosmological magnetic helicity. A peculiar feature of this dynamo equation is that the resistivity depends upon the Ricci scalar curvature. This feature is also present in turbulent dynamo models. Here the electrical effective conductivity is obtained by making use of flat torsion modes of a $R(\Gamma)F^{2}$ Lagrangean where R refers to the Ricci-Cartan spacetime. Power spectrum of the magnetic field is also computed. Lorentz violation appears naturally from birefrigence of photons semi-minimally coupled to torsion. Though Dobado and Maroto [Mod Phys Lett A 12: 3003 (1997)] have previously investigated the role of primordial torsion in the anisotropy of light propagation they made it using the fermionic sector of the QED Lagrangean while we obtained similar results using the photonic sector. They also used the pseudo-trace of torsion while we here work out with the torsion trace itself.Comment: departamento de fisica teorica-UERJ-Rio de Janeiro-Brasi

Neutrino asymmetry in general relativistic rotating radiative stars

Neutrino asymmetry in general relativistic radiative spacetime exterior to spinning stars is investigating by making use of Newmann-Penrose (NP) spin coefficient formalism. It is shown that neutrino current depends on the direction of rotation of the star. The solution is obtained in test field approximation where the neutrinos do not generate gravitational fields.Comment: Latex fil

A teleparallel effective geometry for Einstein's unified field theory

Riemannian and teleparallel geometrical approaches to the investigation of Maxwell electrodynamics shown that a unified field theory of gravitation and electromagnetism a la Einstein can be obtained from a stationary metric. This idea contrasts with the recently proposed pre-metric electrodynamics by Hehl and Obukhov. In the teleparallel case the definition of the electric field is obtained straightforward from the spacetime metric and the orthonormal basis frame of teleparallelism. In this case the only nonvanishing component of Cartan torsion is defined as the effective electric field. In this approach the gravitational potentials or metric coefficients are expressed in terms of the effective or analogous electric and magnetic potentials. Thefore the Maxwell equations in vacuum can be obtained by derivation of this electric field definition as usual. In the Riemannian case we consider an electrostatic spacetime where the Einstein equations in vacuum in the approximation of linear fields. The constraint of Einstein equations in vacuum are shown to lead or to the Coulomb equation or to a singular behaviour on the metric which would represent a kind of effective electrodynamic black hole event horizon.Comment: Latex fil

Cosmological Background torsion limits from Lorentz violation

Cosmological limits on Lorentz invariance breaking in Chern-Simons $(3+1)-dimensional$ electrodynamics are used to place limits on torsion. Birefrigence phenomena is discussed by using extending the propagation equation to Riemann-Cartan spacetimes instead of treating it in purely Riemannian spaces. The parameter of Lorentz violation is shown to be proportional to the axial torsion vector which allows us to place a limit on cosmological background torsion from the Lorentz violation constraint which is given by $10^{-33} eV <|S^{\mu}| < 10^{-32} eV$ where $|S^{\mu}|$ is the axial torsion vector.Comment: Latex fil

Gravitational torsion kinks and thick domain walls

The dynamics of a gravitational torsion kink as a plane symmetric thick domain wall solution of Einstein-Cartan (EC) field equation is given. The spin-torsion energy has to be as high as the gravitational kink potential otherwise torsion will not contribute as an appreciable effect to domain wall.Cartan torsion also contributes to the orthonal pressure of the domain wall.Comment: 5 pages late

Dynamos driven by poloidal flows in untwisted, curved and flat Riemannian diffusive flux tubes

Recently Vishik anti-fast dynamo theorem, has been tested against non-stretching flux tubes [Phys Plasmas 15 (2008)]. In this paper, another anti-dynamo theorem, called Cowling's theorem, which states that axisymmetric magnetic fields cannot support dynamo action, is carefully tested against thick tubular and curved Riemannian untwisted flows, as well as thin flux tubes in diffusive and diffusionless media. In the non-diffusive media the Cowling's theorem is not violated in thin Riemann-flat untwisted flux tubes, where the Frenet curvature is negative. Nevertheless the diffusion action in the thin flux tube leads to a a dynamo action driven by poloidal flows as shown by Love and Gubbins (Geophysical Res.) in the context of geodynamos. Actually it is shown that a slow dynamo action is obtained. In this case the Frenet and Riemann curvature still vanishes. In the case of magnetic filaments in diffusive media dynamo action is obtained when the Frenet scalar curvature is negative. Since the Riemann curvature tensor can be expressed in terms of the Frenet curvature of the magnetic flux tube axis, this result can be analogous to a recent result obtained by Chicone, Latushkin and Smith, which states that geodesic curvature in compact Riemannian manifolds can drive dynamo action in the manifold. It is also shown that in absence of diffusion, magnetic energy does not grow but magnetic toroidal magnetic field can be generated by the poloidal field, what is called a plasma dynamo

Torsion effects on vortex filaments and Hasimoto soliton transformation in magnetars

The role played by torsion of magnetic vortex line curves or filaments, in the equilibrium state of magnetars is investigated. When the magnetars equilibrium equations are written in terms Frenet-Serret frame it is shown that in regions of the magnetic star where the Frenet torsion is constant it induces an oscillation in the vortex filaments. By solving the magnetar equilibrium equation we shown the this behaviour also appears in the magnetic field. The first derivative of the gravitational potential with respect to the arc lenght of the vortex filament is shown to coincide with the Hasimoto soliton transformation of the Schroedinger equation for the constant torsion.Comment: Latex fil

Torsion Strings inside Static Black Holes in Teleparallel Gravity

Cosmic strings inside Schwarzschild black holes in teleparallel gravity are considered.Torsion flux inside the black hole is compute like a torsion vortex on a superfluid.Since some components of torsion are singular on Schwarzschild horizon and others remain finite we compute a torsion invariant to decide whether the torsion is singular and where torsion singularities located.It is found out that as in the curvature case of Einstein's black hole the event horizon is not a mere coordinate singularity for torsion although a true torsion singularity is found at the center of the teleparallel black hole.Torsion flux vanishes along the cosmic string itself.It is shown from Cartan equation in differential forms that the spins inside the black hole are polarized along the torsion string.Torsion string seems to be confined inside the black hole.Comment: Latex fil

Spin polarised particles in Goedel world

The motion of classical test spinning particles in Godel universe in the realm of Einstein's General Relativity (GR) is investigated by making use of Killing conserved currents. We consider three distinct cases of motion of spinning particles polarized along the three distinct axes of the anisotropic metric. It is shown that in the case the spin is polarised along the y-direction the minimum energy of the motion is attained for only for spinless particles while the other two directions the minimum energy is obtained for spinning particles. The continuos energy spectrum is also computed.Comment: Latex fil