The assumption that matter charges and currents could generate fields, which are called, in analogy with electromagnetism, gravitoeletric and gravitomagnetic fields, dating from the origins of General Relativity (GR). On the other hand, the Teleparallel Equivalent of GR (TEGR), as a gauge theory, seems to be the ideal scenario to define these fields, based on the gauge field strength components. The purpose of the present work is to investigate the nature of the gravitational electric and magnetic fields in the context of the TEGR, where the tetrad formalism on which it is based seems more suited to deal with phenomena related to observers. As its applications, we have studied the gravitoelectromagnetic fields for the Schwarzschild solution and for the geometry produced by a spherical rotating shell in slow motion and weak field regime. The expressions obtained, at the linear regime, are very similar to those of electromagnetism.
This work is devoted to present and analyze an expression for the gravitational energymomentum vector in the context of f(T) theories through field equations. Such theories are the analogous counterpart of the well known f(R) theories, except using torsion instead of curvature. We obtain a general expression for the gravitational energymomentum vector in this framework. Using the hypothesis of the isotropy of spacetime, we find the gravitational energy for a closed Universe, since construction of real tetrads that do not constrain the functional form of the Lagrangian density was not possible for an open Universe. Thus we find a vanishing gravitational energy for the tetrad that we have used.
The paper deals with the calculation of the gravitational entropy in the context of teleparallel gravity for de Sitter space-time. In such a theory it is possible to define gravitational energy and pressure; thus we use those expressions to construct the gravitational entropy. We use the temperature as a function of the cosmological constant and write the first law of thermodynamics from which we obtain the entropy. In the limit Λ ≪ 1 we find that the entropy is proportional to volume, for a specific temperature's choice; we find that Δ ≥ 0 as well. We also identify a phase transition in de Sitter space-time by analyzing the specific heat.
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