This review presents a study of the situation when two spacetimes admit the same (unparametrized) geodesics, that is, when they are projectively related. The solution is based on the curvature class and the holonomy type of a spacetime and it transpires that all holonomy possibilities can be solved except the most general one and that the consequence of two spacetimes being projectively related leads, in many cases, to their associated Levi-Civita connections being identical. Some results are also given regarding the general case. It is also shown that the holonomy types of projectively related spacetimes are very closely related. The theory is then applied, with Einstein's principle of equivalence in mind, to 'generic' spacetimes.
- projective structure
- holonomy and general relativity