In the context of a gauge theory for the translation group, we have obtained, for a spinless particle, a gravitational analogue 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 any one 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.

A Lagrangian from which derive the third post-Newtonian (3PN) equations of motion of compact binaries (neglecting the radiation reaction damping) is obtained. The 3PN equations of motion were computed previously by Blanchet and Faye in harmonic coordinates. The Lagrangian depends on the harmonic-coordinate positions, velocities and accelerations of the two bodies. At the 3PN order, the appearance of one undetermined physical parameter λ reflects an incompleteness of the point-mass regularization used when deriving the equations of motion. In addition the Lagrangian involves two unphysical (gauge-dependent) constants r ′ 1 and r ′ 2 parametrizing some logarithmic terms. The expressions of the ten Noetherian conserved quantities, associated with the invariance of the Lagrangian under the Poincaré group, are computed. By performing an infinitesimal "contact" transformation of the motion, we prove that the 3PN harmonic-coordinate Lagrangian is physically equivalent to the 3PN Arnowitt-Deser-Misner Hamiltonian obtained recently by Damour, Jaranowski and Schäfer.

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 Møller's canonical energy-momentum density of the gravitational field.PACS numbers: 04.50. + hThe definition of an energy-momentum density for the gravitational field is one of the oldest and most controversial problems of gravitation. As a true field, it would be natural to expect that gravity should have its own local energy-momentum density. However, it is usually asserted that such a density cannot be locally defined because of the equivalence principle [1]. As a consequence, any attempt to identify an energy-momentum density for the gravitational field leads to complexes that are not true tensors. The first of such attempts was made by Einstein who proposed an expression for the energy-momentum density of the gravitational field which was nothing but the canonical expression obtained from Noether's theorem [2]. Indeed, this quantity is a pseudotensor, an object that depends on the coordinate system. Several other attempts have been made, leading to different expressions for the energy-momentum pseudotensor for the gravitational field [3].Despite the existence of some controversial points related to the formulation of the equivalence principle [4], it seems true that, in the context of general relativity, no tensorial expression for the gravitational energy-momentum density can exist. However, as our results show, in the gauge context, the existence of an expression for the gravitational energy-momentum density which is a true spacetime and gauge tensor turns out to be possible. Accordingly, the absence of such an expression should be attributed to the general relativity description of gravitation, which seems to not be the appropriate framework to deal with this problem [5].In spite of some skepticism [1], there has been a continuous interest in this problem [6]. In particular, a quasilocal approach has been proposed recently which is highly clarifying [7]. According to this approach, for each gravitational energy-momentum pseudotensor, there is an associated superpotential which is a Hamiltonian boundary term. The energy momentum defined by such a pseudotensor does not really depend on the local value of the reference frame, but only on the value of the reference frame on the boundary of a region-then its quasilocal character. As the relevant boundary conditions are physically acceptable, this approach validates the pseudotensor approach to the gravitational energy-momentum problem. It should be mentioned that these results were obtained in the context of the general relativity description of gravitation.In the present work a different approach will be used to reexamine the gravitation...

The fundamentals of the teleparallel equivalent of general relativity are presented, and its main properties described. In particular, the field equations, the definition of an energy-momentum density for the gravitational field, the teleparallel version of the equivalence principle, and the dynamical role played by torsion as compared to the corresponding role played by curvature in general relativity, are discussed in some details.