79 research outputs found

    Teleparallel Killing Vectors of the Einstein Universe

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    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 p+qp+q. 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

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    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

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    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

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    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

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    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 E=18π∫SdΞdϕ(sinΞgΞΞ+gϕϕ−(1/grr)(∂gΞΞgϕϕ/∂r))E=\frac{1}{8\pi}\int_S d\theta d\phi(sin\theta \sqrt{g_{\theta\theta}}+\sqrt{g_{\phi\phi}}-(1/\sqrt{g_{rr}})(\partial{\sqrt{g_ {\theta\theta} g_{\phi\phi}}}/\partial r)). It is surprised to learn that the energy expression is relevant to the metric components grrg_{rr}, gΞΞg_{\theta\theta} and gϕϕg_{\phi\phi} 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

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    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

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    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

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    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

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    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 K=(±1,0)K = (\pm 1, 0)

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    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 K=(−1,0).K = (-1, 0). 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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