Weyl Geometries and Timelike Geodesics

Understand

In view of Ehlers-Pirani-Schild formalism, since 1972 Weyl geometries should be considered to be the most appropriate and complete framework to represent (relativistic) gravitational fields.

• We shall here show that in any given Lorentzian spacetime (M,g) that admits global timelike vector fields any such vector field u determines an essentially unique Weyl geometry ([g], \Gamma) such that u is \Gamma-geodesic (i.e.
• parallel with respect to \Gamma).