Bringing Together Gravity and the Quanta

Due to its underlying gauge structure, teleparallel gravity achieves a separation between inertial and gravitational effects. It can, in consequence, describe the isolated gravitational interaction without resorting to the equivalence principle, and is able to provide a tensorial definition for the energy-momentum density of the gravitational field. Considering the conceptual conflict between the local equivalence principle and the nonlocal uncertainty principle, the replacement of general relativity by its teleparallel equivalent can be considered an important step towards a prospective reconciliation between gravitation and quantum mechanics.Comment: 9 pages. Contribution to the proceedings of the Albert Einstein Century International Conference, Paris, 18-22 July, 200

Teleparallel Spin Connection

A new expression for the spin connection of teleparallel gravity is proposed, given by minus the contorsion tensor plus a zero connection. The corresponding minimal coupling is covariant under local Lorentz transformation, and equivalent to the minimal coupling prescription of general relativity. With this coupling prescription, therefore, teleparallel gravity turns out to be fully equivalent to general relativity, even in the presence of spinor fields.Comment: 2 pages, RevTeX, to appear in Phys. Rev D (Brief Report

Gravitational Energy-Momentum Density in Teleparallel Gravity

In the context of a gauge theory for the translation group, a conserved energy-momentum gauge current for the gravitational field is obtained. It is a true spacetime and gauge tensor, and transforms covariantly under global Lorentz transformations. By rewriting the gauge gravitational field equation in a purely spacetime form, it becomes the teleparallel equivalent of Einstein's equation, and the gauge current reduces to the M{\o}ller's canonical energy-momentum density of the gravitational field.Comment: RevTeX, 4 pages, no figures, to appear in Phys. Rev. Let

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 $E=\frac{1}{8\pi}\int_S d\theta d\phi(sin\theta \sqrt{g_{\theta\theta}}+\sqrt{g_{\phi\phi}}-(1/\sqrt{g_{rr}})(\partial{\sqrt{g_ {\theta\theta} g_{\phi\phi}}}/\partial r))$. It is surprised to learn that the energy expression is relevant to the metric components $g_{rr}$, $g_{\theta\theta}$ and $g_{\phi\phi}$ 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

Teleparallel Equivalent of Non-Abelian Kaluza-Klein Theory

Based on the equivalence between a gauge theory for the translation group and general relativity, a teleparallel version of the non-abelian Kaluza-Klein theory is constructed. In this theory, only the fiber-space turns out to be higher-dimensional, spacetime being kept always four-dimensional. The resulting model is a gauge theory that unifies, in the Kaluza-Klein sense, gravitational and gauge fields. In contrast to the ordinary Kaluza-Klein models, this theory defines a natural length-scale for the compact sub-manifold of the fiber space, which is shown to be of the order of the Planck length.Comment: Revtex4, 7 pages, no figures, to appear in Phys. Rev.