156 research outputs found
An assessment of Evans' unified field theory I
Evans developed a classical unified field theory of gravitation and
electromagnetism on the background of a spacetime obeying a Riemann-Cartan
geometry. This geometry can be characterized by an orthonormal coframe theta
and a (metric compatible) Lorentz connection Gamma. These two potentials yield
the field strengths torsion T and curvature R. Evans tried to infuse
electromagnetic properties into this geometrical framework by putting the
coframe theta to be proportional to four extended electromagnetic potentials A;
these are assumed to encompass the conventional Maxwellian potential in a
suitable limit. The viable Einstein-Cartan(-Sciama-Kibble) theory of gravity
was adopted by Evans to describe the gravitational sector of his theory.
Including also the results of an accompanying paper by Obukhov and the author,
we show that Evans' ansatz for electromagnetism is untenable beyond repair both
from a geometrical as well as from a physical point of view. As a consequence,
his unified theory is obsolete.Comment: 39 pages of latex, modified because of referee report, mistakes and
typos removed, partly reformulated, taken care of M.W.Evans' rebutta
An exact solution of the metric-affine gauge theory with dilation, shear, and spin charges
The spacetime of the metric-affine gauge theory of gravity (MAG) encompasses
{\it nonmetricity} and {\it torsion} as post-Riemannian structures. The sources
of MAG are the conserved currents of energy-momentum and dilation, shear and
spin. We present an exact static spherically symmetric vacuum solution of the
theory describing the exterior of a lump of matter carrying mass and dilation,
shear and spin charges.Comment: 13 pages, RevTe
An assessment of Evans' unified field theory II
Evans developed a classical unified field theory of gravitation and
electromagnetism on the background of a spacetime obeying a Riemann-Cartan
geometry. In an accompanying paper I, we analyzed this theory and summarized it
in nine equations. We now propose a variational principle for Evans' theory and
show that it yields two field equations. The second field equation is algebraic
in the torsion and we can resolve it with respect to the torsion. It turns out
that for all physical cases the torsion vanishes and the first field equation,
together with Evans' unified field theory, collapses to an ordinary Einstein
equation.Comment: 11 pages of late
On the theory of the skewon field: From electrodynamics to gravity
The Maxwell equations expressed in terms of the excitation and the field strength are metric-free and require an
additional constitutive law in order to represent a complete set of field
equations. In vacuum, we call this law the ``spacetime relation''. We assume it
to be local and linear. Then encompasses 36
permittivity/permeability functions characterizing the electromagnetic
properties of the vacuum. These 36 functions can be grouped into 20+15+1
functions. Thereof, 20 functions finally yield the dilaton field and the metric
of spacetime, 1 function represents the axion field, and 15 functions the
(traceless) skewon field \notS_i{}^j (S slash), with . The
hypothesis of the existence of \notS_i{}^j was proposed by three of us in
2002. In this paper we discuss some of the properties of the skewon field, like
its electromagnetic energy density, its possible coupling to Einstein-Cartan
gravity, and its corresponding gravitational energy.Comment: latex-file, 15 pages, 1 figur
Torsion as electromagnetism and spin
We show that it is possible to formulate the classical Einstein-Maxwell-Dirac
theory of spinors interacting with the gravitational and electromagnetic fields
as the Einstein-Cartan-Kibble-Sciama theory with the Ricci scalar of the
traceless torsion, describing gravity, and the torsion trace acting as the
electromagnetic potential.Comment: 6 pages; published versio
Spin and Rotation in General Relativity
Rapporteur's Introduction to the GT8 session of the Ninth Marcel Grossmann
Meeting (Rome, 2000); to appear in the Proceedings.Comment: LaTeX file, no figures, 15 page
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 and a torsion field 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
yields (undesirable) modifications of the Maxwell equations. The second class
of the type 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
Big bounce from spin and torsion
The Einstein-Cartan-Sciama-Kibble theory of gravity naturally extends general
relativity to account for the intrinsic spin of matter. Spacetime torsion,
generated by spin of Dirac fields, induces gravitational repulsion in fermionic
matter at extremely high densities and prevents the formation of singularities.
Accordingly, the big bang is replaced by a bounce that occurred when the energy
density was on the order of (in
natural units), where is the fermion number density and is
the number of thermal degrees of freedom. If the early Universe contained only
the known standard-model particles (), then the energy density at
the big bounce was about 15 times larger than the Planck energy. The minimum
scale factor of the Universe (at the bounce) was about times smaller
than its present value, giving \approx 50 \mum. If more fermions existed in
the early Universe, then the spin-torsion coupling causes a bounce at a lower
energy and larger scale factor. Recent observations of high-energy photons from
gamma-ray bursts indicate that spacetime may behave classically even at scales
below the Planck length, supporting the classical spin-torsion mechanism of the
big bounce. Such a classical bounce prevents the matter in the contracting
Universe from reaching the conditions at which a quantum bounce could possibly
occur.Comment: 6 pages; 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
Four-fermion interaction from torsion as dark energy
The observed small, positive cosmological constant may originate from a
four-fermion interaction generated by the spin-torsion coupling in the
Einstein-Cartan-Sciama-Kibble gravity if the fermions are condensing. In
particular, such a condensation occurs for quark fields during the
quark-gluon/hadron phase transition in the early Universe. We study how the
torsion-induced four-fermion interaction is affected by adding two terms to the
Dirac Lagrangian density: the parity-violating pseudoscalar density dual to the
curvature tensor and a spinor-bilinear scalar density which measures the
nonminimal coupling of fermions to torsion.Comment: 6 pages; published versio
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