Gravitomagnetismo e o teste da sonda gravidade B

The so-called gravitomagnetic field arised as an old conjecture that currents of matter (no charges) would produce gravitational effects similar to those produced by electric currents in electromagnetism. Hans Thirring in 1918, using the weak field approximation to the Einsteins field equations, deduced that a slowly rotating massive shell drags the inertial frames in the direction of its rotation. In the same year, Joseph Lense applied to astronomy the calculations of Thirring. Later, that effect came to be known as the Lense- Thirring effect. Along with the de Sitter effect, those phenomena were recently tested by a gyroscope in orbit around the Earth, as proposed by George E. Pugh in 1959 and Leonard I. Schiff in 1960. In this dissertation, we study the gravitational effects associated with the rotation of massive bodies in the light of the Einsteins General Theory of Relativity. With that finality, we develop the weak field approximation to General Relativity and obtain the various associated gravitational effects: gravitomagnetic time-delay, de Sitter effect (geodesic precession) and the Lense-Thirring effect (drag of inertial frames). We discus the measures of the Lense-Thirring effect done by LAGEOS Satellite (Laser Geodynamics Satellite) and the Gravity Probe B - GPB - mission. The GPB satellite was launched into orbit around the Earth at an altitude of 642 km by NASA in 2004. Results presented in May 2011 clearly show the existence of the Lense-Thirring effect- a drag of inertial frames of 37:2 7:2 mas/year (mas = milliarcsec)- and de Sitter effect - a geodesic precession of 6; 601:8 18:3 mas/year- measured with an accuracy of 19 % and of 0.28 % respectively (1 mas = 4:84810��9 radian). These results are in a good agreement with the General Relativity predictions of 41 mas/year for the Lense-Thirring effect and 6,606.1 mas/year for the de Sitter effect.

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.

The Teleparallel Lagrangian and Hamilton-Jacobi formalism

We analyze the Teleparallel Equivalent of General Relativity (TEGR) from the point of view of Hamilton-Jacobi approach for singular systems.

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.

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.

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.

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.

Some remarks on the coupling prescription of teleparallel gravity

By using a nonholonomic moving frame version of the general covariance principle, an active version of the equivalence principle, an analysis of the gravitational coupling prescription of teleparallel gravity is made. It is shown that the coupling prescription determined by this principle is always equivalent with the corresponding prescription of general relativity, even in the presence of fermions. An application to the case of a Dirac spinor is made.

Torsion and the gravitational interaction

By using a nonholonomous-frame formulation of the general covariance principle, seen as an active version of the strong equivalence principle, an analysis of the gravitational coupling prescription in the presence of curvature and torsion is made. The Coupling prescription implied by this principle is found to be always equivalent to that of general relativity, a result that reinforces the completeness of this theory, as well as the teleparallel point of view according to which torsion does not represent additional degrees of freedom for gravity, but simply an alternative way of representing the gravitational field.