MG13 - Talk detail

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Abstract

We consider Weyl geometry as a representation for space-time and characterize the observers’ proper-time consistently with a geometric formulation for gravitation in this type of geometry. Next, we restrict Weyl geometry to its integrable case (WIST), where the expression for proper-time gives rise to the concept of an effective metric and we set the coupling with other physical fields in a way that gravity acquires gauge symmetry. The role of the effective metric is illustrated from a static and spherically symmetric vacuum solution. Afterwards, we consider an arbitrary Lagrangian for the new field introduced by Weyl and show that the resulting equations for the effective metric are exactly the same obtained for the usual metric by General Relativity (GR) in the presence of a scalar field. We conclude that proper-time requires an appropriate characterization according to the geometry at issue and that, when this is done in WIST, we obtain a natural way to consider scalar fields in GR. Finally, we observe the need to interpret alternative theories of gravity, such as f(R) in the Palatini approach, according to the considerations made.

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