Teleparallel Theory Of Gravity Research Articles

Energy and Momentum Densities of Cosmological Models, with Equation of State ρ=μ, in General Relativity and Teleparallel Gravity

We calculated the energy and momentum densities of stiff fluid solutions, using Einstein, Bergmann–Thomson and Landau–Lifshitz energy-momentum complexes, in both general relativity and teleparallel gravity. In our analysis we get different results comparing the aforementioned complexes with each other when calculated in the same gravitational theory, either this is in general relativity and teleparallel gravity. However, interestingly enough, each complex’s value is the same either in general relativity or teleparallel gravity. Our results sustain that (i) general relativity or teleparallel gravity are equivalent theories (ii) different energy-momentum complexes do not provide the same energy and momentum densities neither in general relativity nor in teleparallel gravity. In the context of the theory of teleparallel gravity, the vector and axial-vector parts of the torsion are obtained. We show that the axial-vector torsion vanishes for the space-time under study.

Wormhole Solution and Energy in Teleparallel Theory of Gravity

An exact solution is obtained in the tetrad theory of gravitation. This solution is characterized by two parameters k1, k2 of spherically symmetric static Lorentzian wormhole which is obtained as a solution of the equation ρ = ρt = 0 with ρ = Ti,ju u , ρt = (Tij − 12Tgij)uiuj , where uui = −1. From this solution which contains an arbitrary function we can generate the other two solutions obtained before. The associated metric of this space-time is a static Lorentzian wormhole and it includes the Schwarzschild black hole, a family of naked singularity and a disjoint family of Lorentzian wormholes. Calculating the energy content of this tetrad field and using the gravitational energy momentum given by Moller in the teleparallel space-time we find that the resulting form depends on the arbitrary function and does not depend on the two parameters k1 and k2 characterizing the wormhole. Using the regularized expression of the gravitational energy momentum we get the value of energy which does not depend on the arbitrary function.

DIFFERENT APPROACHES FOR MØLLER'S ENERGY IN THE KASNER-TYPE SPACETIME

Considering the Møller energy definition in both Einstein's theory of general relativity and tele-parallel theory of gravity, we find the energy of the universe based on viscous Kasner-type metrics. The energy distribution which includes both the matter and gravitational field is found to be zero in both of these different gravitation theories and this result agrees with previous works of Cooperstock and Israelit et al., Banerjee–Sen, Vargas who investigated the problem of the energy in Friedmann–Robertson–Walker universe in Einstein's theory of general relativity and Aydogdu–Saltı who considered the same problem in tele-parallel gravity. In all of these works, they found that the energy of the Friedmann–Robertson–Walker spacetime is zero. Our result is the same as that obtained in the studies of Saltı and Havare. They used the viscous Kasner-type metric and found the total energy and momentum by using Bergmann–Thomson energy–momentum formulation in both general relativity and tele-parallel gravity. The result that the total energy and momentum components of the universe is zero supports the viewpoints of Albrow and Tryon.

Lessons of spin and torsion: Reply to “Consistent coupling to Dirac fields in teleparallelism”

In reply to the criticism made by Mielke in the pereceding Comment [Phys. Rev. D69 (2004) 128501] on our recent paper, we once again explicitly demonstrate the inconsistency of the coupling of a Dirac field to gravitation in the teleparallel equivalent of general relativity. Moreover, we stress that the mentioned inconsistency is generic for {\it all} sources with spin and is by no means restricted to the Dirac field. In this sense the $SL(4,R)$-covariant generalization of the spinor fields in the teleparallel gravity theory is irrelevant to the inconsistency problem.

Metric-affine approach to teleparallel gravity

The teleparallel gravity theory, treated physically as a gauge theory of translations, naturally represents a particular case of the most general gauge-theoretic model based on the general affine group of spacetime. On the other hand, geometrically, the Weitzenb\"ock spacetime of distant parallelism is a particular case of the general metric-affine spacetime manifold. These physical and geometrical facts offer a new approach to teleparallelism. We present a systematic treatment of teleparallel gravity within the framework of the metric-affine theory. The symmetries, conservation laws and the field equations are consistently derived, and the physical consequences are discussed in detail. We demonstrate that the so-called teleparallel GR-equivalent model has a number of attractive features which distinguishes it among the general teleparallel theories, although it has a consistency problem when dealing with spinning matter sources.

Teleparallel origin of the Fierz picture for spin-2 particle

A new approach to the description of a spin-2 particle in flat and curved spacetime is developed on the basis of the teleparallel gravity theory. We show that such an approach is in fact a true and natural framework for the Fierz representation proposed recently by Novello and Neves. More specifically, we demonstrate how the teleparallel theory fixes uniquely the structure of the Fierz tensor, discover the transparent origin of the gauge symmetry of the spin-2 model, and derive the linearized Einstein operator from the fundamental identity of the teleparallel gravity. In order to cope with the consistency problem on the curved spacetime, similarly to the usual Riemannian approach, one needs to include the nonminimal (torsion dependent) coupling terms.

Energy-Momentum and Angular Momentum Carried by Gravitational Waves in Extended New General Relativity

In an extended, new form of general relativity, which is a teleparallel theory of gravity, we examine the energy-momentum and angular momentum carried by gravitational wave radiated from Newtonian point masses in a weak-field approximation. The resulting wave form is identical to the corresponding wave form in general relativity, which is consistent with previous results in teleparallel theory. The expression for the dynamical energy-momentum density is identical to that for the canonical energy-momentum density in general relativity up to leading order terms on the boundary of a large sphere including the gravitational source, and the loss of dynamical energy-momentum, which is the generator of \emph{internal} translations, is the same as that of the canonical energy-momentum in general relativity. Under certain asymptotic conditions for a non-dynamical Higgs-type field $\psi^{k}$, the loss of ``spin'' angular momentum, which is the generator of \emph{internal} $SL(2,C)$ transformations, is the same as that of angular momentum in general relativity, and the losses of canonical energy-momentum and orbital angular momentum, which constitute the generator of Poincar\'{e} \emph{coordinate} transformations, are vanishing. The results indicate that our definitions of the dynamical energy-momentum and angular momentum densities in this extended new general relativity work well for gravitational wave radiations, and the extended new general relativity accounts for the Hulse-Taylor measurement of the pulsar PSR1913+16.

Gauge invariance in teleparallel gravity theories: A solution to the background structure problem

We deal with the problem of identifying a background structure and its perturbation in tetrad theories of gravity. Starting from a peculiar trivial principal bundle we define a metric which depends only on the gauge connection. We find the allowed four-dimensional structure groups; two of them turn out to be the translation group ${T}_{4}$ and the unitary group $U(2).$ When the curvature vanishes the metric reduces to its background form which coincides with the Minkowski flat metric for the ${T}_{4}$ case and with the Einstein static universe metric for the $U(2)$ case. The perturbation has a coordinate independent definition and allows the introduction of observables distinguished from those obtained from the metric alone. Finally, we show that any teleparallel theory of gravity, and hence general relativity, can be considered as a gauge theory over the groups introduced.

Teleparallel complex gravity as foundation for noncommutative gravity

We present a teleparallel complex gravity as the foundation for the formulation of noncommutative gravity theory. The negative energy ghosts in the conventional formulation with U(1,3) local Lorentz connection no longer exists, since the local Lorentz invariance is broken down to U(1,3) global Lorentz symmetry. As desired, our teleparallel complex gravity theory also passes the key classical test of perihelion advance of Mercury. Based on this result, we present a Lagrangian for the noncommutative teleparallel gravity theory.