Teorias da gravitação e geometria de Weyl

• Autor(a) principal: Pucheu, María Laura
• Data de Publicação: 2013
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UFPB
• Texto Completo: https://repositorio.ufpb.br/jspui/handle/tede/9565
• topic: Relatividade Geral; Geometria Riemanniana; Geometria de Weyl inte­grable; Convencionalismo; Teoria gravitacional de Brans-Dicke; General Relativity; Riemannian geometry; Integrable Weyl geometry; Conven­tionalism; Brans-Dicke theory of Gravitation; CIENCIAS EXATAS E DA TERRA::FISICA

We show that the theory of General Relativity can be entirely formulated in the language of the integrable Weyl geometry. We develop the concept of Weyl frames and state the fact that they are completely equivalent as far as geodesic motion is concerned. In the case of General Relativity, we build an action that is manifestly invariant with respect to Weyl transformations. In this scenario, the gravitational field is described by a combination of both the metric and a geometrical scalar field. We illustrate this point by examining how distinct geometrical and physical pictures of the same phenomena may arise in different frames for the particular case of conformally flat spacetimes. Besides, we show that our choice of Weyl geometry for describing the space-time of General Relativity completely agrees with Poincare ideas that the geometry of space was merely a convention and that no geometry is more correct than any other, only more convenient. On the other hand, we consider the Brans-Dicke gravitational theory as a point of departure for constructing a geometric scalar-field theory. In this approach we apply the Palatini variational method to the Brans-Dicke action. We then are naturally led to conclude that space-time has the geometrical structure of a Weyl integrable manifold. We briefly examine some features of this scalar-tensor theory in which Brans-Dicke scalar field now plays the role of a geometrical field.