Teoria da gravitação em Espaços-tempos de Weyl e os Testes do Sistema Solar

Abstract

Assuming that the space-time is endowed with a non-Riemannian geometry given by a Weyl manifold, we formulate a theory of gravitation which generalizes General Relativity and is invariant under Weyl transformations. First, we obtain the gravitational field equations in a Weyl integrable space-time from a variational principle. Second, we generalize both the geodesic s postulates and the clock s postulate to deal with the motion of test particles and light beams that follow the auto-parallels curves of Weyl integrable space-time, called Weyl geodesics. Thirdly, we discussed the question of invariance under Weyl transformations and introduce the concepts of representations of the gravitational field and the notions ofWeyl frame (gauge) and Einstein frame (gauge). Fourth, we obtain the Newtonian limit of the theory. Fifth, we discuss the symmetries of Weyl integrable space-times and the issue of constants of motion related to Weyl geodesics. Finally, we present a solution of the field equations which represents a static and spherically symmetric gravitational field in a Weyl frame and compute the same effects of the gravitational field used as tests of General Relativity in the Solar System, where we get the same results of General Relativity but now related to both the metric and the Weyl scalar field.