On the notions of gravitational and centrifugal force in static spherically symmetric space-times

We present an assessment of some recent suggestions for performing a split between gravitational and inertial forces in general relativity. We prove, by considering a family of simple static space-times, that any such split leads necessarily to a centrifugal force that points in the direction of the local, rather than global, outward direction. We also show that Abramowicz' expression for the centrifugal force emerges spontaneously when separating the variables in the Hamilton-Jacobi and Klein-Gordon equations. Furthermore, we explain in some detail why the whole idea is not necessarily in contradiction with the equivalence principle