Sparling two-forms, the conformal factor and the gravitational energy density of the teleparallel equivalent of general relativity

It has been shown recently that within the framework of the teleparallel equivalent of general relativity (TEGR) it is possible to define the energy density of the gravitational field. The TEGR amounts to an alternative formulation of Einstein's general relativity, not to an alternative gravity theory. The localizability of the gravitational energy has been investigated in a number of space-times with distinct topologies, and the outcome of these analises agree with previously known results regarding the exact expression of the gravitational energy, and/or with the specific properties of the space-time manifold. In this article we establish a relationship between the expression for the gravitational energy density of the TEGR and the Sparling two-forms, which are known to be closely connected with the gravitational energy. We also show that our expression of energy yields the correct value of gravitational mass contained in the conformal factor of the metric field.Comment: 12 pages, Latex file, no figures, to be published in Gen. Rel. Gra

On reference frames in spacetime and gravitational energy in freely falling frames

We consider the interpretation of tetrad fields as reference frames in spacetime. Reference frames may be characterized by an antisymmetric acceleration tensor, whose components are identified as the inertial accelerations of the frame (the translational acceleration and the frequency of rotation of the frame). This tensor is closely related to gravitoelectromagnetic field quantities. We construct the set of tetrad fields adapted to observers that are in free fall in the Schwarzschild spacetime, and show that the gravitational energy-momentum constructed out of this set of tetrad fields, in the framework of the teleparallel equivalent of general relatrivity, vanishes. This result is in agreement with the principle of equivalence, and may be taken as a condition for a viable definition of gravitational energy.Comment: 19 pages, no figures, accepted by Classical and Quantum Gravit

Graviton resonances on two-field thick branes

This work presents new results about the graviton massive spectrum in two-field thick branes. Analyzing the massive spectra with a relative probability method we have firstly showed the presence of resonance structures and obtained a connection between the thickness of the defect and the lifetimes of such resonances. We obtain another interesting results considering the degenerate Bloch brane solutions. In these thick brane models, we have the emergence of a splitting effect controlled by a degeneracy parameter. When the degeneracy constant tends to a critical value, we have found massive resonances to the gravitational field indicating the existence of modes highly coupled to the brane. We also discussed the influence of the brane splitting effect over the resonance lifetimes.Comment: 15 pages, 8 figure

Gravity localization on hybrid branes

This work deals with gravity localization on codimension-1 brane worlds engendered by compacton-like kinks, the so-called hybrid branes. In such scenarios, the thin brane behaviour is manifested when the extra dimension is outside the compact domain, where the energy density is non-trivial, instead of asymptotically as in the usual thick brane models. The zero mode is trapped in the brane, as required. The massive modes, although are not localized in the brane, have important phenomenological implications such as corrections to the Newton's law. We study such corrections in the usual thick domain wall and in the hybrid brane scenarios. By means of suitable numerical methods, we attain the mass spectrum for the graviton and the corresponding wavefunctions. The spectra possess the usual linearly increasing behaviour from the Kaluza-Klein theories. Further, we show that the 4D gravitational force is slightly increased at short distances. The first eigenstate contributes highly for the correction to the Newton's law. The subsequent normalized solutions have diminishing contributions. Moreover, we find out that the phenomenology of the hybrid brane is not different from the usual thick domain wall. The use of numerical techniques for solving the equations of the massive modes is useful for matching possible phenomenological measurements in the gravitational law as a probe to warped extra dimensions.Comment: 15 pages, 11 figure