Weyl Geometry as Characterization of Space-Time

Abstract

Motivated by an axiomatic approach to characterize space-time it is investigated a reformulation of Einstein's gravity where the pseudo-riemannian geometry is substituted by a Weyl one. It is presented the main properties of the Weyl geometry and it is shown that it gives extra contributions to the trajectories of test particles, serving as one more motivation to study general relativity in Weyl geometry. It is introduced its variational formalism and it is established the coupling with other physical fields in such a way that the theory acquires a gauge symmetry for the geometrical fields. It is shown that this symmetry is still present for the red-shift and it is concluded that for cosmological models it opens the possibility that observations can be fully described by the new geometrical scalar field. It is concluded then that this reformulation, although representing a theoretical advance, still needs a complete description of their objects.

12 pages

Cited by in corpus (7)

• General Relativity and Weyl Geometry
• From Brans-Dicke gravity to a geometrical scalar-tensor theory
• Acceleration in Weyl integrable spacetime
• FLRW cosmology in Weyl-Integrable Space-Time
• An Invariant Approach to Weyl's unified field theory
• Clusters of galaxies in a Weyl geometric approach to gravity
• A scalar field inducing a non-metrical contribution to gravitational acceleration and a compatible add-on to light deflection