Remarks concerning the notion of free fall in axiomatic space-time theory

The notion of free fall plays a central role in EPS axiomatics. A constructive procedure for the detection of freely falling gravitational monopoles has been elaborated by Coleman and Korté. This was done in order to eliminate the vagueness of the primitive notion of free fall from spacetime theory. In this paper it is shown that neither the gravitational monopoles nor their free fall can be detected by the proposed procedure alone, without using physical laws beyond the mentioned spacetime theories. For this purpose, two examples of geodesic directing fields in a Schwarzschild space time are presented, one for particles obeying a special Lorentz-force equation and one for objects obeying Papapetrou's spinning particle equation. Two possibilities are discussed to overcome the difficulties of the constructive procedure.