Um estudo sobre a energia do campo gravitacional em espaços-tempo estáticos e esfericamente simétricos no contexto do teleparalelismo - Rodrigues, Marcos Lucena (2025)
The theory of general relativity does not offer in a satisfactory way a definition of the gravitational energy-momentum tensor. The alternative formulation of the gravity, known as the teleparallel equivalent of general relativity, based on the Weitzenböck geometry and whose fundamental field is the tetrad field, arises as an possible solution to this problem. Therefore, based on the field equations of the teleparallel equivalent of general relativity, this master’s thesis proposes to study the static and spherically symmetric spacetime energy and to verify the consistency of the results. As an approach to analysis, we calculate the gravitational and spacetime energy-momentum tensor to these spacetime and focus on two particular cases: Reissner-Nordström-de Sitter black hole and a regular black hole with a magnetic charge in the context of nonlinear electrodynamics. The results obtained were fully consistent to what we expected: the 4−momentum only have temporal component and both spacetime and gravitational energy flux vanishes. In the case of Reissner-Nordström-de Sitter spacetime, we confirm the compatibility of our results with the first law of black holes thermodynamics, and that the gravitational energy density is always negative. Furthermore, we obtain that the gravitational energy density per length has the same value to all the horizons; but for the density of the spacetime, this only occurs when Q = 0. In the regular black holes case, we find that the spacetime energy tends to ADM energy in the limit of r going to infinity and that both pressure and energy density of spacetime are negative to an certain value of r.