REVERSAL OF FORCE AND ENERGY COUPLING AROUND A ROTATING BLACK-HOLE

The net force acting on a test particle orbiting around a rotating black hole reverses its sign several times, as opposed to just once around a rotating Newtonian star. Recently, this behaviour has been explained in terms of reversal of the centrifugal force near a black hole or in terms of increase of the gravitational attraction below the photon orbit. We show that the phenomenon could be understood from the general relativistic coupling of various 'Newtonian' energy terms. In this case, one need not alter the concept of the centrifugal or the gravitational force from that provided by Newtonian physics. The new effects due to the non-linearity could be qualitatively reproduced in Newtonian geometry by, for example, introducing a quadrupole moment to the Newtonian star.