Abstract
Considering the definition of inertial forces acting on a test particle, following non-circular geodesics, in static and stationary space–times, we show that the centrifugal force reversal occurs only in the case of particles following prograde orbits around black holes. We first rewrite the covariant expressions for the acceleration components in terms of the lapse function, shift vector and the three-metric γij, using the ADM 3 + 1 splitting and use these, for different cases as given by pure radial motion, pure azimuthal motion and the general non-circular motion. It is found that the reversal occurs between 2m and 3m, only when the azimuthal angular velocity of the particle supersedes the radial velocity, which indeed depends upon the physical parameters E, ℓ and the Kerr parameter a.
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