Da Teoria de Gauge métrica-afim da gravitação ao teleparalelismo generalizado: equações de campo e a energia gravitacional

Abstract

This dissertation proposes a generalization of the teleparallel equivalent of general relativity based on the metric-affine gauge theory of gravitation (MAG). Furthermore, the relation between the teleparallel frame and the affine connection is analyzed, and a study of the gravitational energy problem is carried out. By applying the variational formalism of MAG, a geometric model is constructed that has degrees of freedom associated with torsion and nonmetricity, and it is shown that it reproduces Einstein’s equations. The analysis of the teleparallel frame shows that teleparallel theories without nonmetricity have bases with a constant scalar product as their teleparallel frame, while theories without torsion use coordinate bases. With regard to the gravitational energy problem, definitions of the 4-momentum and of the energy-momentum tensors of the gravitational field and spacetime are developed. The application of the formalism to the case of plane-fronted gravitational waves (pp-waves) provides results consistent with those found in the literature. These results indicate that generalized teleparallelism is suitable for the analysis of gravitational field energy and allows greater flexibility in choosing the teleparallel frame.