L. C. Garcia de Andrade

On dilaton solutions of de Sitter inflation and primordial spin-torsion density fluctuations

Abstract Four classes of exact solutions of Einstein-Cartan dilatonic inflationary de Sitter cosmology are given. The first is obtained from the equation of state of massless dilaton instead of an unpolarized fermion fluid used previously by Gasperini. Repulsive gravity is found in the case where dilatons are constraint by the presence of spin-torsion effects. The second and third solutions represent respectively massive dilatons in the radiation era with the massive potential and torsion kinks and finally the dust of spinning particles. Primordial spin-density fluctuations are also computed based on Primordial fluctuations of temperature obtained from COBE data. The temperature fluctuation can also be computed from the nearly flat spectrum of the gravitational waves produced during inflation and by the result that the dilaton mass would be proportional to the Hubble constant. This result agrees with the COBE data. This idea is also used to compute the spin-torsion density in the inflation era.

On Non-Riemannian Domain Walls

Two classes of non-Riemannian domain walls are obtained as distributional planar sources for the linearized Einstein-Cartan (EC) field equations of gravity. The first class represents spin polarized particles distributed on the non-Minkowskian side of the wall and an analogy with the ferromagnetic domains is displayed since the spin distributions are different on both sides of the walls. The other class represents a gravitational analog of Type I superconductor where Cartan torsion plays the role of the magnetic field. The “interior” solution is obtained by using matching conditions in EC-gravity and is matched to a torsionless vacuum in the last case.

Riemannian geometry of twisted magnetic flux tubes in almost helical plasma flows

Riemannian geometry of curves applied recently by Ricca [Fluid Dyn. Res 36, 319 (2005)] in the case of inflectional disequilibrium of twisted magnetic flux tubes is used here to compute the magnetic helicity force-free field case. Here the application of Lorentz force-free to the magnetic flux tube in tokamaks allows one to obtain an equation that generalizes the cylindrical tokamak equation by a term that contains the curvature of the magnetic flux tube. Another example of the use of the magnetic flux tube is done by taking the electron magnetohydrodynamics (MHD) fluid model (EMHD) of plasma physics that allows one to compute the velocity of the fluid in helical and almost helical flows in terms of the Frenet torsion of thin magnetic flux tubes. The cases of straight and curved twisted tubes are examined. Second-order effects on the Frenet torsion arise on the poloidal component of the magnetic field, while curvature effects appear in the toroidal component. The magnetic fields are computed in terms of t...

Space-time defects: Torsion walls

The geometry of torsion defects in Weitzenbock space–time is investigated. Conformal de Sitter space–time outside the defect is obtained. Geodesic motion of test particles outside the torsion wall is given. Torsion defect wall is shown to have repulsive gravitational fields. Static torsion defect is obtained by gluing together two half Minkowski spaces across a torsion wall junction.

Vortex filaments in MHD

Two theorems on the Riemannian geometrical constraints on vortex magnetic filaments acting as dynamos in (MHD) flows are presented. The use of Gauss–Mainard–Codazzi equations allows us to investigate in detail the influence of curvature and torsion of vortex filaments in the MHD dynamos. This application follows closely previous applications to Heisenberg spin equation to the investigations in magnetohydrostatics given by Schief (2003 Plasma Phys. J. 10 2677). The Lorentz forces on vortex filaments are computed and the ratios between the forces along different directions are obtained in terms of the ratio between the corresponding magnetic fields which also equals the ratio between the Frenet torsion and vortex line curvature. A similar relation between Lorentz forces, magnetic fields and twist, which is proportional to total torsion integral, has been obtained by Ricca (2005 Fluid Dyn. Res. 36 319) in the case of inflexional disequilibrium of magnetic flux tubes. This is due to the fact that the magnetic vortex lines are a limiting case of the magnetic flux tubes when the length of the tube is much greater than the radius of the tube. The magnetic helicity equation of the filament allows us again to determine the magnetic fields ratio from Frenet curvature and torsion of the vortex lines. Recently, Schekochihin et al (2001 Phys. Rev. E 65 016305) obtained a similar relation between the ratios of magnetic field components by using a detailed analysis of the statistics of curvature. However, in their work no reference is made to torsion or helical vortex filaments.

TORSION BOUNDS FROM CP VIOLATION α2-DYNAMO IN AXION–PHOTON COSMIC PLASMA

Years ago Mohanty and Sarkar [Phys. Lett. B433, 424 (1998)] have placed bounds on torsion mass from K meson physics. In this paper, associating torsion to axions a la Campanelli et al. [Phys. Rev. D72, 123001 (2005)], it is shown that it is possible to place limits on spacetime torsion by considering an efficient α2-dynamo CP violation term. Therefore instead of Kostelecky et al. [Phys. Rev. Lett.100, 111102 (2008)] torsion bounds from Lorentz violation, here torsion bounds are obtained from CP violation through dynamo magnetic field amplification. It is also shown that oscillating photon–axion frequency peak is reduced to 10-7Hz due to torsion mass (or Planck mass when torsion does not propagate) contribution to the photon–axion–torsion action. Though torsion does not couple to electromagnetic fields at classical level, it does at the quantum level. Recently, Garcia de Andrade [Phys. Lett. B468, 28 (2011)] has shown that the photon sector of Lorentz violation (LV) Lagrangian leads to linear nonstandard Maxwell equations where the magnetic field decays slower giving rise to a seed for galactic dynamos. Torsion constraints of the order of K0≈10-42GeV can be obtained which are more stringent than the value obtained by Kostelecky et al. A lower bound for the existence of galactic dynamos is obtained for torsion as K0≈10-37GeV.

Stretch fast dynamo mechanism via conformal mapping in Riemannian manifolds

Two new analytical solutions of the self-induction equation in Riemannian manifolds are presented. The first represents a twisted magnetic flux tube or flux rope in plasma astrophysics, where the rotation of the flow implies that the poloidal field is amplified from toroidal field, in the spirit of dynamo theory. The value of the amplification depends on the Frenet torsion of the magnetic axis of the tube. Actually this result illustrates the Zeldovich stretch, twist, and fold method to generate dynamos from straight and untwisted ropes. Based on the fact that this problem was previously handled, using a Riemannian geometry of twisted magnetic flux ropes [Phys Plasmas 13, 022309 (2006)], investigation of a second dynamo solution, conformally related to the Arnold kinematic fast dynamo, is obtained. In this solution, it is shown that the conformal effect on the fast dynamo metric enhances the Zeldovich stretch, and therefore a new dynamo solution is obtained. When a conformal mapping is performed in an Arn...

On the necessity of non-Riemannian acoustic spacetime in fluids with vorticity

The necessity of a newly proposed [L.C. Garcia de Andrade, Phys. Rev. D 70 (2004) 64004] non-Riemannian acoustic spacetime structure called acoustic torsion of sound wave equation in fluids with vorticity are discussed. It is shown that this structure, although not always necessary is present in fluids with vorticity even when the perturbation is rotational. This can be done by solving the Bergliaffa et al. [Physica D 191 (2004) 121] gauge invariant equations for sound, superposed to a general background flow, needs to support a non-Riemannian acoustic geometry in effective spacetime. Bergliaffa et al. have previously shown that a Riemannian structure cannot be associated to this gauge invariant general system.

Letter: Spin Polarised Magnetized Cylinders in Torsioned Spacetime

A Spin-polarised cylindrically symmetric exact class of solutions endowed with magnetic fields in Einstein-Cartan-Maxwell gravity is obtained. Application of matching conditions to this interior solution having an exterior as Einsteins vacuum solution shows that for this class of metrics the Riemann-Cartan (RC) rotation vanishes which makes the solution static. Therefore we end up with a magnetized static spin polarised cylinder where the pressure along the symmetry axis is negative.A Spin-polarised cylindrically symmetric exact class of solutions endowed with magnetic fields in Einstein-Cartan-Maxwell gravity is obtained. Application of matching conditions to this interior solution having an exterior as Einsteins vacuum solution shows that for this class of metrics the Riemann-Cartan (RC) rotation vanishes which makes the solution static. Therefore we end up with a magnetized static spin polarised cylinder where the pressure along the symmetry axis is negative.

COSMIC RELIC TORSION FROM INFLATIONARY COSMOLOGY

An inflationary de Sitter solution of Teleparallel Equivalent of General Relativity (TERG) is obtained. In this model Cartan torsion is shown to be a cosmological relic in the sense that it decays from earlier epochs of the Universe until extremely small values at the present epoch. This would be the reason why it is very difficult to measure cosmological torsion at the present epoch and only extremely small relic torsion would be left. Torsion plays a role similar to the inflaton field in its interaction with the scalar field. The torsion mass is determined from the teleparallel action in terms of the Planck mass. The value of the torsion mass is of the order of Planck mass. An upper limit for torsion of 10-18s-1 is obtained for the de Sitter phase. By considering the Friedmann phase it is possible to show that torsion induces an oscillation on the Universe.