This is a corrigendum for the paper under the title above and whose reference is Garcia de Andrade (2001 Class. Quantum Grav. 18 3907). In this paper, a wrong formula (44) between the proportionality between the magnetic field of a spin-polarized cylinder in Einstein-Cartan-Maxwell gravity and the spinpolarized density or Cartan spacetime torsion, is corrected. This correction is shown to produce several interesting physical consequences as that this spinpolarized cylinder produces a primordial magnetic field B ∼ 10 −22 G which is able to seed galactic dynamos. The mistake does not modify the external metric to the string-like configuration. Several important physical consequences may come out from this correction.Keywords: torsion, dynamos, strings, Einstein-Cartan gravity, cosmology Earlier the author published a paper in CQG [1] where spin-polarized cylinders with magnetic fields were used as a tool to test Einstein-Cartan theory of gravitation [2]. Unfortunately, recently we have discovered an important mistake in two formulas which we hereby correct. The importance of this correction is proved through an example on the computation of the primordial magnetic field on this string-like source which is shown to yield a seed magnetic field able to produce galactic magnetic fields from galactic dynamo mechanism [3], as recently discussed by this author [4]. The basic reason for this is the fact that the mistake is exactly in formulas (43) and (44), of that paper, which we repeat here as 0264-9381/14/079501+03$33.00
Two new analytical solutions of self-induction equation, in Riemannian manifolds are presented. The first represents a twisted magnetic flux tube or flux rope in plasma astrophysics, which shows that the depending on rotation of the flow the poloidal field is amplified from toroidal field which represents a dynamo. 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 (STF) method to generate dynamos from straight and untwisted ropes. Motivated by the fact that this problem was treated using a Riemannian geometry of twisted magnetic flux ropes recently developed (Phys Plasmas (2006)), we investigated a second dynamo solution which is conformally related to the Arnold kinematic fast dynamo. In this solution it is shown that the conformal effect on the fast dynamo metric only enhances the Zeldovich stretch, and therefore a new dynamo solution is obtained. When a conformal mapping is performed in Arnold fast dynamo line element a uniform stretch is obtained in the original line element. PACS numbers: 02.40.Hw-Riemannian geometries
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.
Vishik's antidynamo theorem is applied to non-stretched twisted magnetic flux tube in Riemannian space. Marginal or slow dynamos along curved (folded), torsioned (twisted) and non-stretching flux tubes plasma flows are obtained. Riemannian curvature of twisted magnetic flux tube is computed in terms of the Frenet curvature in the thin tube limit. It is shown that, for non-stretched filaments fast dynamo action in diffusive case cannot be obtained, in agreement with Vishik's argument, that fast dynamo cannot be obtained in non-stretched flows. In this case a non-uniform stretching slow dynamo is obtained.An example is given which generalizes plasma dynamo laminar flows, recently presented by Wang et al [Phys Plasmas (2002)], in the case of low magnetic Reynolds number Re m ≥ 210. Curved and twisting Riemannian heliotrons, where non-dynamo modes are found even when stretching is presented, shows that the simple presence of stretching is not enough for the existence of dynamo action. Folding is equivalent to Riemann curvature and can be used to cancell magnetic fields, not enhancing the dynamo action. In this case nondynamo modes are found for certain values of torsion or Frenet curvature (folding) in the spirit of anti-dynamo theorem. It is shown that curvature and stretching are fundamental for the existence of fast dynamos in plasmas.PACS numbers: 02.40.Hw:differential geometries. 91.25.Cw-dynamo theories.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.