Observer fields in Weylian spacetime models

Abstract

Resting upon the Ehlers-Pirani-Schild axiomatic approach to spacetime theory, the author considers Weyl manifolds as reasonable spacetime models. He defines and discuss several concepts associated with a timelike vector field (=observer field=reference frame) on such a spacetime model. In particular, he derives propagation equations for rotation, expansion and shear of V, prove some kinematical vorticity theorems and present a new method how to measure length curvature operationally. As important mathematical tools, he uses the orthogonal decomposition of the Lie derivative and of the covariant derivative; the latter is the Weylian generalization of the Fermi-Walker derivative.