941 research outputs found
The Einstein static universe with torsion and the sign problem of the cosmological constant
In the field equations of Einstein-Cartan theory with cosmological constant a
static spherically symmetric perfect fluid with spin density satisfying the
Weyssenhoff restriction is considered. This serves as a rough model of space
filled with (fermionic) dark matter. From this the Einstein static universe
with constant torsion is constructed, generalising the Einstein Cosmos to
Einstein-Cartan theory.
The interplay between torsion and the cosmological constant is discussed. A
possible way out of the cosmological constant's sign problem is suggested.Comment: 8 pages, LaTeX; minor layout changes, typos corrected, one new
equation, new reference [5], completed reference [13], two references adde
Test Matter in a Spacetime with Nonmetricity
Examples in which spacetime might become non-Riemannian appear above Planck
energies in string theory or, in the very early universe, in the inflationary
model. The simplest such geometry is metric-affine geometry, in which {\it
nonmetricity} appears as a field strength, side by side with curvature and
torsion. In matter, the shear and dilation currents couple to nonmetricity, and
they are its sources. After reviewing the equations of motion and the Noether
identities, we study two recent vacuum solutions of the metric-affine gauge
theory of gravity. We then use the values of the nonmetricity in these
solutions to study the motion of the appropriate test-matter. As a
Regge-trajectory like hadronic excitation band, the test matter is endowed with
shear degrees of freedom and described by a world spinor.Comment: 14 pages, file in late
PP-waves with torsion and metric-affine gravity
A classical pp-wave is a 4-dimensional Lorentzian spacetime which admits a
nonvanishing parallel spinor field; here the connection is assumed to be
Levi-Civita. We generalise this definition to metric compatible spacetimes with
torsion and describe basic properties of such spacetimes. We use our
generalised pp-waves for constructing new explicit vacuum solutions of
quadratic metric-affine gravity.Comment: 17 pages, LaTeX2
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 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
A formal framework for a nonlocal generalization of Einstein's theory of gravitation
The analogy between electrodynamics and the translational gauge theory of
gravity is employed in this paper to develop an ansatz for a nonlocal
generalization of Einstein's theory of gravitation. Working in the linear
approximation, we show that the resulting nonlocal theory is equivalent to
general relativity with "dark matter". The nature of the predicted "dark
matter", which is the manifestation of the nonlocal character of gravity in our
model, is briefly discussed. It is demonstrated that this approach can provide
a basis for the Tohline-Kuhn treatment of the astrophysical evidence for dark
matter.Comment: 13 pages RevTex, no figures; v2: minor corrections, reference added,
matches published versio
Autoparallels From a New Action Principle
We present a simpler and more powerful version of the recently-discovered
action principle for the motion of a spinless point particle in spacetimes with
curvature and torsion. The surprising feature of the new principle is that an
action involving only the metric can produce an equation of motion with a
torsion force, thus changing geodesics to autoparallels. This additional
torsion force arises from a noncommutativity of variations with parameter
derivatives of the paths due to the closure failure of parallelograms in the
presence of torsionComment: Paper in src. Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html Read paper directly
with Netscape under
http://www.physik.fu-berlin.de/~kleinert/kleiner_re243/preprint.htm
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