http://arxiv.org/abs/2201.03076
In this paper we discuss on recent attempts aimed at demonstrating that the second clock effect (SCE) does not take place in Weyl spaces, which is contrary to well-known results. These attempts include Weyl gauge theories of gravity, as well as the symmetric teleparallel theories (STTs). Our approach to this issue is based on the power of Weyl gauge symmetry (WGS) which is a manifest symmetry of the basic laws of Weyl geometry. Through proper consideration of WGS we shall show that the SCE, being an effect of purely geometric nature, does not depend on the chosen theory of gravity and matter. Quite the contrary, the SCE singles out those matter couplings which are phenomenologically compatible with the underlying geometric laws. Here we consider both, spacetimes based in Weyl geometry with arbitrary nonmetricity (generalized Weyl geometry), as well as, standard Weyl spaces where the nonmetricity is proportional to the product of a Weyl gauge vector by the metric. This issue is of special relevance for the fate of the STTs which are being intensively applied in the cosmological framework. As we shall show, if realize that WGS is a manifest symmetry of generalized Weyl spaces, neither the Weyl gauge theories nor the STTs are free of the second clock effect, unless Weyl integrable geometry (WIG) spaces are considered.
I. Quiros
Tue, 11 Jan 22
29/95
Comments: 16 pages, no figures