Energy for moving mass up a centrifugal gravity barrier

Hi,



I have been pondering on this -



what is the energy required to move a point mass m from a radial position R to the center of a rotating frame, if the linear velocity v of the point mass at position R is relativistic (close to c).



For an observer in the rotating frame, it should seem as if m is climbing against the centrifugal gravity. In the classical limit, the answer is [itex]\frac{mv^2}{2}[/itex]





Thanks!