Centrifugal and Coriolis Force Components Acting on a Fluid Element in a Curved Space Time

Defining the four vectors n and τ of Abramowicz’s covariant formalism of inertial forces, in terms of the lapse function α, shift vector β, the metric γij and the velocity 3-vector V , we derive the components of centrifugal and Coriolis accelerations acting on a fluid element with four velocity U. We show that while for purely radial flow the centrifugal acceleration component is zero in static space time, for purely azimuthal flow it is exactly same as in the case of a test particle. However, when both radial and azimuthal components of 3-velocity are non-zero, the centrifugal acceleration shows no reversal outside the event horizon in Schwarzschild geometry.