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

General relativity on a null surface: Hamiltonian formulation in the teleparallel geometry

The Hamiltonian formulation of general relativity on a null surface is established in the teleparallel geometry. No particular gauge conditons on the tetrads are imposed, such as the time gauge condition. By means of a 3+1 decomposition the resulting Hamiltonian arises as a completely constrained system. However, it is structurally different from the the standard Arnowitt-Deser-Misner (ADM) type formulation. In this geometrical framework the basic field quantities are tetrads that transform under the global SO(3,1) and the torsion tensor.Comment: 15 pages, Latex, no figures, to appear in the Gen. Rel. Gra

Neutron Stars in Teleparallel Gravity

In this paper we deal with neutron stars, which are described by a perfect fluid model, in the context of the teleparallel equivalent of general relativity. We use numerical simulations to find the relationship between the angular momentum of the field and the angular momentum of the source. Such a relation was established for each stable star reached by the numerical simulation once the code is fed with an equation of state, the central energy density and the ratio between polar and equatorial radii. We also find a regime where linear relation between gravitational angular momentum and moment of inertia (as well as angular velocity of the fluid) is valid. We give the spatial distribution of the gravitational energy and show that it has a linear dependence with the squared angular velocity of the source.Comment: 19 pages, 14 figures. arXiv admin note: text overlap with arXiv:1206.331

Three-dimensional Dirac oscillator in a thermal bath

The thermal properties of the three-dimensional Dirac oscillator are considered. The canonical partition function is determined, and the high-temperature limit is assessed. The degeneracy of energy levels and their physical implications on the main thermodynamic functions are analyzed, revealing that these functions assume values greater than the one-dimensional case. So that at high temperatures, the limit value of the specific heat is three times bigger.Comment: 9 pages, 4 figures. Text improved, references added. Revised to match accepted version in Europhysics Letters