Quadratic gravity in (2+1)D with a topological Chern-Simons term

Three-dimensional quadratic gravity, unlike general relativity in (2+1)D, is dynamically nontrivial and has a well behaved nonrelativistic potential. Here we analyse the changes that occur when a topological Chem-Simons term is added to this theory. It is found that the harmless massive scalar mode of the latter gives rise to a troublesome massive spin-0 ghost, while the massive spin-2 ghost is replaced by two massive physical particles both of spin 2. We also found that light deflection does not have the 'wrong sign' such as in the framework of three-dimensional quadratic gravity.

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 with the ordinary Kaluza-Klein models, this theory defines a natural length scale for the compact submanifold of the fiber space, which is shown to be of the order of the Planck length.

The energy of the universe in teleparallel gravity

The teleparallel versions of the Einstein and the Landau-Lifshitz energy-momentum complexes of the gravitational field are obtained. By using these complexes, the total energy of the universe, which includes the energy of both the matter and the gravitational fields, is then obtained. It is shown that in the case of a closed universe, the total energy vanishes independently of the pseudotensor used, as well as of the three dimensionless coupling constants of teleparallel gravity.

Tree-level violation of the equivalence principle

Massive particles of spin 0 and 1 violate the equivalence principle (EP) at the tree level. on the other hand, if these particles are massless, they agree with the EP, which leads us to conjecture that from a semiclassical viewpoint massless particles, no matter what their spin, obey the EP. General relativity predicts a deflection angle of 2.63' for a nonrelativistic spinless massive boson passing close to the Sun, while for a massive vectorial boson of spin 1 the corresponding deflection is 2.62'.

Spin 1 fields in Riemann-Cartan space-times via Duffin-Kemmer-Petiau theory

We consider massive spin 1 fields, in Riemann-Cartan space-times, described by Duffin-Kemmer-Petiau theory. We show that this approach induces a coupling between the spin 1 field and the space-time torsion which breaks the usual equivalence with the Proca theory, but that such equivalence is preserved in the context of the Teleparallel Equivalent of General Relativity.

Gravitational rainbow of massive particles

Photon propagation is non-dispersive within the context of semiclassical general relativity. What about the remaining massless particles? It can be shown that at the tree level the scattering of massless particles of spin 0, 1/2, 1 or whatever by a static gravitational field generated by a localized source such as the Sun, treated as an external field, is non-dispersive as well. It is amazing, however, that massive particles, regardless of whether they have integral or half-integral spin, experience an energy-dependent gravitational deflection. Therefore, semiclassical general relativity and gravitational rainbows of massive particles can coexist without conflict. We address this issue in this essay.

Godel type solution in teleparallel gravity

The stationary cosmological model without closed timelike curves of Godel type is obtained for the ideal dust matter source within the framework of the teleparallel gravity. For a specific choice of the teleparallel gravity parameters, this solution reproduces the causality violating stationary Godel solution in general relativity, in accordance with the teleparallel equivalent of general relativity. The relation between the axial-vector torsion and the cosmic vorticity is clarified. (C) 2004 Elsevier B.V. All rights reserved.

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

In reply to the criticism made by Mielke in the preceding Comment 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 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.

Regge calculus in teleparallel gravity

In the context of the teleparallel equivalent of general relativity, the Weitzenbock manifold is considered as the limit of a suitable sequence of discrete lattices composed of an increasing number of smaller and smaller simplices, where the interior of each simplex (Delaunay lattice) is assumed to be flat. The link lengths l between any pair of vertices serve as independent variables, so that torsion turns out to be localized in the two-dimensional hypersurfaces (dislocation triangle, or hinge) of the lattice. Assuming that a vector undergoes a dislocation in relation to its initial position as it is parallel transported along the perimeter of the dual lattice (Voronoi polygon), we obtain the discrete analogue of the teleparallel action, as well as the corresponding simplicial vacuum field equations.

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 telepaxallel gravity or general relativity.

Covariance properties and regularization of conserved currents in tetrad gravity

We discuss the properties of the gravitational energy-momentum 3-form within the tetrad formulation of general relativity theory. We derive the covariance properties of the quantities describing the energy-momentum content under Lorentz transformations of the tetrad. As an application, we consider the computation of the total energy (mass) of some exact solutions of Einstein's general relativity theory which describe compact sources with asymptotically flat spacetime geometry. As it is known, depending on the choice of tetrad frame, the formal total integral for such configurations may diverge. We propose a natural regularization method which yields finite values for the total energy-momentum of the system and demonstrate how it works on a number of explicit examples.

Some remarks on the neutrino oscillation phase in a gravitational field

The weak gravitational field expansion method to account for the gravitationally induced neutrino oscillation effect is critically examined, then it is shown that the splitting of the neutrino phase into a kinematic and a gravitational phase is not always possible because the relativistic factor modifies the particle interference phase splitting condition in a gravitational field.

Angular momentum and energy-momentum densities as gauge currents

If we replace the general spacetime group of diffeomorphisms by transformations taking place in the tangent space, general relativity can be interpreted as a gauge theory, and in particular as a gauge theory for the Lorentz group. In this context, it is shown that the angular momentum and the energy-momentum tensors of a general matter field can be obtained from the invariance of the corresponding action integral under transformations taking place, not in spacetime, but in the tangent space, in which case they can be considered as gauge currents.

Kerr-Newman solution as a Dirac particle

For m(2) < a(2) + q(2), with m, a, and q respectively the source mass, angular momentum per unit mass, and electric charge, the Kerr-Newman (KN) solution of Einstein's equation reduces to a naked singularity of circular shape, enclosing a disk across which the metric components fail to be smooth. By considering the Hawking and Ellis extended interpretation of the KN spacetime, it is shown that, similarly to the electron-positron system, this solution presents four inequivalent classical states. Making use of Wheeler's idea of charge without charge, the topological structure of the extended KN spatial section is found to be highly non-trivial, leading thus to the existence of gravitational states with half-integral angular momentum. This property is corroborated by the fact that, under a rotation of the space coordinates, those inequivalent states transform into themselves only after a 4π rotation. As a consequence, it becomes possible to naturally represent them in a Lorentz spinor basis. The state vector representing the whole KN solution is then constructed, and its evolution is shown to be governed by the Dirac equation. The KN solution can thus be consistently interpreted as a model for the electron-positron system, in which the concepts of mass, charge and spin become connected with the spacetime geometry. Some phenomenological consequences of the model are explored.

Gravitation without the equivalence principle

In the general relativistic description of gravitation, geometry replaces the concept of force. This is possible because of the universal character of free fall, and would break down in its absence. on the other hand, the teleparallel version of general relativity is a gauge theory for the translation group and, as such, describes the gravitational interaction by a force similar to the Lorentz force of electromagnetism, a non-universal interaction. Relying on this analogy it is shown that, although the geometric description of general relativity necessarily requires the existence of the equivalence principle, the teleparallel gauge approach remains a consistent theory for gravitation in its absence.