International Journal of Astronomy and Astrophysics, 2012, 2, 180-182

http://dx.doi.org/10.4236/ijaa.2012.23022 Published Online September 2012 (http://www.SciRP.org/journal/ijaa)

Broken Symmetries in Spacetime with Torsion and

Galactic Magnetic Fields without Dynamo Amplification

Luis Carlos Garcia de Andrade

Department of Theoretical Physics, IF-UERJ, Rio de Janeiro, Maracanã

Emai l: garcia@dft .if.u erj.br

Received February 6, 2012; revised March 15, 2012; accepted March 26, 2012

ABSTRACT

Since Kostelecky et al. [Physical Review Letters 100, 111102 (2008)], have shown that there is an intimate connection

between spacetime with torsion and the possibility of constraining it to Lorentz violation, a renewed interest in torsion

theories of gravity has arised. In this paper, minimal coupling between photons on a torsioned background is shown to

allow us to obtain the galactic magnetic field strength μG without dynamo amplification. This agrees with recent results

by Jimenez and Maroto (2011) for spiral galaxies, with galactic magnetic field constraints from Dark matter without dy-

namo amplification. The approach discussed here allows us to get rid of the unpleasant photon mass by simply consid-

ering the Lagrangean cut off for second order torsion terms. Therefore though the gauge and Lorentz symmetries are

broken here one does not have to deal with photon masses.

Keywords: Star Dynamos; Torsion Theories; Lorentz-Violation; Cosmology; Astro-Particle Physics

1. Introduction

There are many papers where galactic magnetic fields [1]

and not only primordial fields can be obtained from a

Biermann battery type and not from a usual dynamo me-

chanism of magnetic field amplification. More recently

Jimenez and Maroto cite [2] have shown that in the

presence of dark energy, magnetic fields are generated

without any amplification. They obtained for spiral

galaxies fields of the strength of 10–9 G in accordance

with Schuster-Blackett conjecture that the magnetic

fields are obtained from angular momentum. Earlier on

De Sabbata and Gasperini [3] showed that this conjecture

could be placed in the realm of Einstein-Cartan gravity

[4], where spin of the elementary particles are the Cartan

torsion source [5]. More recent Opher and Wichoski [6]

have shown that the same mechanism can be used to

obtain galactic magnetic fields without dynamos ampli-

fication. Also Kostelecky et al. [7] investigated the

Lorentz violation (LV) of the fermionic sector of a Lag-

rangean, in Riemann-Cartan spacetime the curvature

tensor ijkl and the e.m sector Rij kl

F, (i, j = 0, 1, 2, 3)

given by displays the same symmetries of

LV term, where the Riemann-Cartan curvature tensor,

including torsion terms plays the role of the Higgs sector

constants ijkl . The main difference from previous

papers [8] is that one uses here a minimal coupling

instead the non-minimal photon-torsion coupling where

the magnetic vector potential does not interact directly

ij kl

ijkl

RFF

k

with torsion or contortion part in the QED Lagrangean.

In this paper, we show that the use of this photon sector

coupled with torsion flat mode, via non-minimal coup-

ling yields naturally the breaking of gauge fields and a

strength for the galactic magnetic fields of the observed

G

value without the dynamo amplification. Besides

the advantage of the approach here is that by considering

only first order terms on torsion, one is able to avoid the

uncomfortable photon tiny mass. The paper is organised

as follows : In Section 2 we consider the Riemann-Cartan

(RC) sector of the Lagrangean obtain a 2D system of

Maxwell generalised equation which are similar to the

ones obtained for the neutrino mass o scillation. Section 5

contains conclusions and discussions.

2. Flat Photon-Torsion Minimal Coupling

and Magnetic Field Amplification

Since the torsion effects are cosmological weak in the

galaxy formation post inflationary era, compared to cur-

vature effects of Einstein gravity sector, second-order

torsion effects are neglected in the torsioned quantum

electrodynamics (QED). Photon and gravity torsion se-

ctors are given by [9]

1

4*

2

2

**

11

=d 4

ij ij

ij ij

il kij klijk

iklijklik j

SxgFFaRFF

m

bRF FcRF FdDF DF

(1)

C

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