79 research outputs found
Teleparallel Killing Vectors of the Einstein Universe
In this short paper we establish the definition of the Lie derivative of a
second rank tensor in the context of teleparallel theory of gravity and also
extend it for a general tensor of rank . This definition is then used to
find Killing vectors of the Einstein universe. It turns out that Killing
vectors of the Einstein universe in the teleparallel theory are the same as in
General Relativity.Comment: 9 pages, accepted for publication in Mod. Phys. Lett.
Teleparallel Killing Vectors of Spherically Symmetric Spacetimes
In this paper, Killing vectors of spherically spacetimes have been evaluated
in the context of teleparallel theory of gravitation. Further, we investigate
the Killing vectors of the Friedmann metrics. It is found that for static
spherically spacetimes the number of Killing vectors turn out to be
\emph{seven} while for the Friedmann models, we obtain \emph{six} teleparallel
Killing vectors. The results are then compared with those of General
Relativity. We conclude that both of these descriptions of gravity do not
provide the consistent results in general. However, these results may coincide
under certain conditions for a particular spacetime.Comment: 14 pages, accepted for publication in Communications in Theoretical
Physic
Gravitation and Duality Symmetry
By generalizing the Hodge dual operator to the case of soldered bundles, and
working in the context of the teleparallel equivalent of general relativity, an
analysis of the duality symmetry in gravitation is performed. Although the
basic conclusion is that, at least in the general case, gravitation is not dual
symmetric, there is a particular theory in which this symmetry shows up. It is
a self dual (or anti-self dual) teleparallel gravity in which, due to the fact
that it does not contribute to the interaction of fermions with gravitation,
the purely tensor part of torsion is assumed to vanish. The ensuing fermionic
gravitational interaction is found to be chiral. Since duality is intimately
related to renormalizability, this theory may eventually be more amenable to
renormalization than teleparallel gravity or general relativity.Comment: 7 pages, no figures. Version 2: minor presentation changes,
references added. Accepted for publication in Int. J. Mod. Phys.
Fourth order gravity: equations, history, and applications to cosmology
The field equations following from a Lagrangian L(R) will be deduced and
solved for special cases. If L is a non-linear function of the curvature
scalar, then these equations are of fourth order in the metric. In the
introduction we present the history of these equations beginning with the paper
of H. Weyl from 1918, who first discussed them as alternative to Einstein's
theory. In the third part, we give details about the cosmic no hair theorem,
i.e., the details how within fourth order gravity with L= R + R^2 the
inflationary phase of cosmic evolution turns out to be a transient attractor.
Finally, the Bicknell theorem, i.e. the conformal relation from fourth order
gravity to scalar-tensor theory, will be shortly presented.Comment: 51 pages, LaTeX, no figure, lecture for 42nd Karpacz Winter School
6.-11.2.06, references 99-109 and related comments are adde
Energy of general 4-dimensional stationary axisymmetric spacetime in the teleparallel geometry
The field equation with the cosmological constant term is derived and the
energy of the general 4-dimensional stationary axisymmetric spacetime is
studied in the context of the hamiltonian formulation of the teleparallel
equivalent of general relativity (TEGR). We find that, by means of the integral
form of the constraints equations of the formalism naturally without any
restriction on the metric parameters, the energy for the asymptotically flat/de
Sitter/Anti-de Sitter stationary spacetimes in the Boyer-Lindquist coordinate
can be expressed as . It is surprised to learn that the
energy expression is relevant to the metric components ,
and only. As examples, by using this formula
we calculate the energies of the Kerr-Newman (KN), Kerr-Newman Anti-de Sitter
(KN-AdS), Kaluza-Klein, and Cveti\v{c}-Youm spacetimes.Comment: 12 page
Riemannian and Teleparallel Descriptions of the Scalar Field Gravitational Interaction
A comparative study between the metric and the teleparallel descriptions of
gravitation is made for the case of a scalar field. In contrast to the current
belief that only spin matter could detect the teleparallel geometry, scalar
matter being able to feel the metric geometry only, we show that a scalar field
is able not only to feel anyone of these geometries, but also to produce
torsion. Furthermore, both descriptions are found to be completely equivalent,
which means that in fact, besides coupling to curvature, a scalar field couples
also to torsion.Comment: Minor corrections made, and a paragraph added to the last section.
Version to appear in Gen. Rel. Gra
Space-time defects and teleparallelism
We consider the class of space-time defects investigated by Puntigam and
Soleng. These defects describe space-time dislocations and disclinations
(cosmic strings), and are in close correspondence to the actual defects that
arise in crystals and metals. It is known that in such materials dislocations
and disclinations require a small and large amount of energy, respectively, to
be created. The present analysis is carried out in the context of the
teleparallel equivalent of general relativity (TEGR). We evaluate the
gravitational energy of these space-time defects in the framework of the TEGR
and find that there is an analogy between defects in space-time and in
continuum material systems: the total gravitational energy of space-time
dislocations and disclinations (considered as idealized defects) is zero and
infinit, respectively.Comment: 22 pages, no figures, to appear in the Class. Quantum Gravit
Axial-Vector Torsion and the Teleparallel Kerr Spacetime
In the context of the teleparallel equivalent of general relativity, we
obtain the tetrad and the torsion fields of the stationary axisymmetric Kerr
spacetime. It is shown that, in the slow rotation and weak field
approximations, the axial-vector torsion plays the role of the gravitomagnetic
component of the gravitational field, and is thus the responsible for the
Lense-Thirring effect.Comment: 9 pages, no figures, to appear in Class. Quant. Gra
Gravitational Lorentz Force and the Description of the Gravitational Interaction
In the context of a gauge theory for the translation group, we have obtained,
for a spinless particle, a gravitational analog of the Lorentz force. Then, we
have shown that this force equation can be rewritten in terms of magnitudes
related to either the teleparallel or the riemannian structures induced in
spacetime by the presence of the gravitational field. In the first case, it
gives a force equation, with torsion playing the role of force. In the second,
it gives the usual geodesic equation of General Relativity. The main conclusion
is that scalar matter is able to feel anyone of the above spacetime geometries,
the teleparallel and the metric ones. Furthermore, both descriptions are found
to be completely equivalent in the sense that they give the same physical
trajectory for a spinless particle in a gravitational field.Comment: Equations (44)-(47) correcte
Mach's principle: Exact frame-dragging via gravitomagnetism in perturbed Friedmann-Robertson-Walker universes with
We show that the dragging of the axis directions of local inertial frames by
a weighted average of the energy currents in the universe is exact for all
linear perturbations of any Friedmann-Robertson-Walker (FRW) universe with K =
(+1, -1, 0) and of Einstein's static closed universe. This includes FRW
universes which are arbitrarily close to the Milne Universe, which is empty,
and to the de Sitter universe. Hence the postulate formulated by E. Mach about
the physical cause for the time-evolution of the axis directions of inertial
frames is shown to hold in cosmological General Relativity for linear
perturbations. The time-evolution of axis directions of local inertial frames
(relative to given local fiducial axes) is given experimentally by the
precession angular velocity of gyroscopes, which in turn is given by the
operational definition of the gravitomagnetic field. The gravitomagnetic field
is caused by cosmological energy currents via the momentum constraint. This
equation for cosmological gravitomagnetism is analogous to Ampere's law, but it
holds also for time-dependent situtations. In the solution for an open universe
the 1/r^2-force of Ampere is replaced by a Yukawa force which is of identical
form for FRW backgrounds with The scale of the exponential
cutoff is the H-dot radius, where H is the Hubble rate, and dot is the
derivative with respect to cosmic time. Analogous results hold for energy
currents in a closed FRW universe, K = +1, and in Einstein's closed static
universe.Comment: 23 pages, no figures. Final published version. Additional material in
Secs. I.A, I.J, III, V.H. Additional reference
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