539 research outputs found
Volume elements of spacetime and a quartet of scalar fields
Starting with a `bare' 4-dimensional differential manifold as a model of
spacetime, we discuss the options one has for defining a volume element which
can be used for physical theories. We show that one has to prescribe a scalar
density \sigma. Whereas conventionally \sqrt{|\det g_{ij}|} is used for that
purpose, with g_{ij} as the components of the metric, we point out other
possibilities, namely \sigma as a `dilaton' field or as a derived quantity from
either a linear connection or a quartet of scalar fields, as suggested by
Guendelman and Kaganovich.Comment: 7 pages RevTEX, submitted to Phys. Rev.
A teleparallel model for the neutrino
The main result of the paper is a new representation for the Weyl Lagrangian
(massless Dirac Lagrangian). As the dynamical variable we use the coframe, i.e.
an orthonormal tetrad of covector fields. We write down a simple Lagrangian -
wedge product of axial torsion with a lightlike element of the coframe - and
show that variation of the resulting action with respect to the coframe
produces the Weyl equation. The advantage of our approach is that it does not
require the use of spinors, Pauli matrices or covariant differentiation. The
only geometric concepts we use are those of a metric, differential form, wedge
product and exterior derivative. Our result assigns a variational meaning to
the tetrad representation of the Weyl equation suggested by J.B.Griffiths and
R.A.Newing.Comment: 4 pages, REVTe
Regge Calculus in Teleparallel Gravity
In the context of the teleparallel equivalent of general relativity, the
Weitzenbock manifold is considered as the limit of a suitable sequence of
discrete lattices composed of an increasing number of smaller an smaller
simplices, where the interior of each simplex (Delaunay lattice) is assumed to
be flat. The link lengths between any pair of vertices serve as independent
variables, so that torsion turns out to be localized in the two dimensional
hypersurfaces (dislocation triangle, or hinge) of the lattice. Assuming that a
vector undergoes a dislocation in relation to its initial position as it is
parallel transported along the perimeter of the dual lattice (Voronoi polygon),
we obtain the discrete analogue of the teleparallel action, as well as the
corresponding simplicial vacuum field equations.Comment: Latex, 10 pages, 2 eps figures, to appear in Class. Quant. Gra
Gravity on a parallelizable manifold. Exact solutions
The wave type field equation \square \vt^a=\la \vt^a, where \vt^a is a
coframe field on a space-time, was recently proposed to describe the gravity
field. This equation has a unique static, spherical-symmetric,
asymptotically-flat solution, which leads to the viable Yilmaz-Rosen metric. We
show that the wave type field equation is satisfied by the pseudo-conformal
frame if the conformal factor is determined by a scalar 3D-harmonic function.
This function can be related to the Newtonian potential of classical gravity.
So we obtain a direct relation between the non-relativistic gravity and the
relativistic model: every classical exact solution leads to a solution of the
field equation. With this result we obtain a wide class of exact, static
metrics. We show that the theory of Yilmaz relates to the pseudo-conformal
sector of our construction. We derive also a unique cosmological (time
dependent) solution of the described type.Comment: Latex, 17 page
A gauge theoretical view of the charge concept in Einstein gravity
We will discuss some analogies between internal gauge theories and gravity in
order to better understand the charge concept in gravity. A dimensional
analysis of gauge theories in general and a strict definition of elementary,
monopole, and topological charges are applied to electromagnetism and to
teleparallelism, a gauge theoretical formulation of Einstein gravity.
As a result we inevitably find that the gravitational coupling constant has
dimension , the mass parameter of a particle dimension ,
and the Schwarzschild mass parameter dimension l (where l means length). These
dimensions confirm the meaning of mass as elementary and as monopole charge of
the translation group, respectively. In detail, we find that the Schwarzschild
mass parameter is a quasi-electric monopole charge of the time translation
whereas the NUT parameter is a quasi-magnetic monopole charge of the time
translation as well as a topological charge. The Kerr parameter and the
electric and magnetic charges are interpreted similarly. We conclude that each
elementary charge of a Casimir operator of the gauge group is the source of a
(quasi-electric) monopole charge of the respective Killing vector.Comment: LaTeX2e, 16 pages, 1 figure; enhanced discussio
Torsion and the Gravitational Interaction
By using a nonholonomous-frame formulation of the general covariance
principle, seen as an active version of the strong equivalence principle, an
analysis of the gravitational coupling prescription in the presence of
curvature and torsion is made. The coupling prescription implied by this
principle is found to be always equivalent with that of general relativity, a
result that reinforces the completeness of this theory, as well as the
teleparallel point of view according to which torsion does not represent
additional degrees of freedom for gravity, but simply an alternative way of
representing the gravitational field.Comment: Version 2: minor presentation changes, a reference added, 11 pages
(IOP style
Poincar\'e gauge theory with even and odd parity dynamic connection modes: isotropic Bianchi cosmological models
The Poincar\'e gauge theory of gravity has a metric compatible connection
with independent dynamics that is reflected in the torsion and curvature. The
theory allows two good propagating spin-0 modes. Dynamical investigations using
a simple expanding cosmological model found that the oscillation of the 0
mode could account for an accelerating expansion similar to that presently
observed. The model has been extended to include a mode and more
recently cross parity couplings. We investigate the dynamics of this model in a
situation which is simple, non-trivial, and yet may give physically interesting
results that might be observable. We consider homogeneous cosmologies, more
specifically, isotropic Bianchi class A models. We find an effective Lagrangian
for our dynamical system, a system of first order equations, and present some
typical dynamical evolution.Comment: 8 pages, 1 figures, submitted to IARD 2010 Conference Proceedings in
{\em Journal of Physics: Conference Series}, eds. L. Horwitz and M. Land
(2011
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