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 Møller's canonical energy-momentum density of the gravitational field.

Gravitational energy of Kerr and Kerr anti-de Sitter space-times in the teleparallel geometry

In the context of the hamiltonian formulation of the teleparallel equivalent of general relativity we compute the gravitational energy of Kerr and Kerr Anti-de Sitter (Kerr-AdS) space-times. The present calculation is carried out by means of an expression for the energy of the gravitational field that naturally arises from the integral form of the constraint equations of the formalism. In each case, the energy is exactly computed for finite and arbitrary spacelike two-spheres, without any restriction on the metric parameters. In particular, we evaluate the energy at the outer event horizon of the black holes. © SISSA/ISAS 2003.

The equivalence principle revisited

A precise fomulation of the strong Equivalence Principle is essential to the understanding of the relationship between gravitation and quantum mechanics. The relevant aspects are reviewed in a context including General Relativity but allowing for the presence of torsion. For the sake of brevity, a concise statement is proposed for the Principle: An ideal observer immersed in a gravitational field can choose a reference frame in which gravitation goes unnoticed. This statement is given a clear mathematical meaning through an accurate discussion of its terms. It holds for ideal observers (time-like smooth non-intersecting curves), but not for real, spatially extended observers. Analogous results hold for gauge fields. The difference between gravitation and the other fundamental interactions comes from their distinct roles in the equation of force.

Torsion and gravitation: A new view

According to the teleparallel equivalent of general relativity, curvature and torsion are two equivalent ways of describing the same gravitational field. Though equivalent, they act differently: curvature yields a geometric description, in which the concept of gravitational force is absent whereas torsion acts as a true gravitational force, quite similar to the Lorentz force of electrodynamics. As a consequence, the right-hand side of a spinless-particle equation of motion (which would represent a gravitational force) is always zero in the geometric description, but not in the teleparallel case. This means that the gravitational coupling prescription can be minimal only in the geometric case. Relying on this property, a new gravitational coupling prescription in the presence of curvature and torsion is proposed. It is constructed in such a way to preserve the equivalence between curvature and torsion, and its basic property is to be equivalent to the usual coupling prescription of general relativity. According to this view, no new physics is connected with torsion, which is just an alternative to curvature in the description of gravitation. An application of this formulation to the equations of motion of both a spinless and a spinning particle is discussed.

Wakes in dilatonic current-carrying cosmic strings

In this work, we present the gravitational field generated by a cosmic string carrying a timelike current in the scalar-tensor gravities. The mechanism of formation and evolution of wakes is fully investigated in this framework. We show explicitly that the inclusion of electromagnetic properties for the string induces logarithmic divergences in the accretion problem.

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.

Prediction of R plus R-2 gravity for the deflection of a photon passing close to the Sun

The cross-section for the scattering of a photon by the Sun's gravitational field, treated as an external field, is computed in the framework of R + R-2 gravity. Using this result, we found that for a photon just grazing the Sun's surface the deflection is 1.75 which is exactly the same as that given by Einstein's theory. An explanation for this pseudo-paradox is provided.

Cosmological constant and the speed of light

By exploring the relationship between the propagation of electromagnetic waves in a gravitational field and the light propagation in a refractive medium, it is shown that, in the presence of a positive cosmological constant, the velocity of light will be smaller than its special relativity value. Then, restricting again to the domain of validity of geometrical optics, the same result is obtained in the context of wave optics. It is argued that this phenomenon and the anisotropy in the velocity of light in a gravitational field are produced by the same mechanism.

Light deflection and quadratic gravity

We study the bending of light caused by a static gravitational field generated by a localized material source in the context of quadratic gravity. Our calculation shows that for light rays passing close to the Sun the deflection Phi lies in the interval 0 < < 1.75. A tree-level approach to the same issue tells us that the vacuum concerning quadratic gravity is a dispersive medium. Nom Phi is energy dependent and ranges from 0(+) to 1.75(-) arcsec.

Axial-vector torsion and the teleparallel Kerr spacetime

In the context of the teleparallel equivalent of general relativity, we obtain the tetrad and the torsion fields of the stationary axisymmetric Kerr spacetime. It is shown that, in the slow rotation and weak-field approximations, the axial-vector torsion plays the role of the gravitomagnetic component of the gravitational field, and is thus responsible for the Lense-Thirring effect.

Gravitation as anholonomy

A gravitational field can be seen as the anholonomy of the tetrad fields. This is more explicit in the teleparallel approach, in which the gravitational field-strength is the torsion of the ensuing Weitzenbock connection. In a tetrad frame, that torsion is just the anholonomy of that frame. The infinitely many tetrad fields taking the Lorentz metric into a given Riemannian metric differ by point-dependent Lorentz transformations. Inertial frames constitute a smaller infinity of them, differing by fixed-point Lorentz transformations. Holonomic tetrads take the Lorentz metric into itself, and correspond to Minkowski flat spacetime. An accelerated frame is necessarily anholonomic and sees the electromagnetic field strength with an additional term.

Torsion gravity: A reappraisal

The role played by torsion in gravitation is critically reviewed. After a description of the problems and controversies involving the physics of torsion, a comprehensive presentation of the teleparallel equivalent of general relativity is made. According to this theory, curvature and torsion are alternative ways of describing the gravitational field, and consequently related to the same degrees of freedom of gravity. However, more general gravity theories, like for example Einstein-Cartan and gauge theories for the Poincare and the affine groups, consider curvature and torsion as representing independent degrees of freedom. By using an active version of the strong equivalence principle, a possible solution to this conceptual question is reviewed. This solution ultimately favors the teleparallel point of view, and consequently the completeness of general relativity. A discussion of the consequences for gravitation is presented.

Bending of light in the framework of R + R2 gravity

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Cosmic acceleration from second order gauge gravity

We construct a phenomenological theory of gravitation based on a second order gauge formulation for the Lorentz group. The model presents a long-range modification for the gravitational field leading to a cosmological model provided with an accelerated expansion at recent times. We estimate the model parameters using observational data and verify that our estimative for the age of the Universe is of the same magnitude than the one predicted by the standard model. The transition from the decelerated expansion regime to the accelerated one occurs recently (at similar to 9.3 Gyr).

Quantum mechanics versus equivalence principle

We consider the scattering of a photon by a weak gravitational field, treated as an external field, up to second order of the perturbation expansion. The resulting cross section is energy dependent which indicates a violation of Galileo's equivalence principle (universality of free fall) and, consequently, of the classical equivalence principle. The deflection angle theta for a photon passing by the sun is evaluated afterward and the likelihood of detecting Delta theta/theta(E) theta-theta(E)/theta(E) (where theta(E) is the value predicted by Einstein's geometrical theory for the light bending) in the foreseeable future, is discussed.