Centrifugal force and ellipticity behaviour of a slowly rotating ultra-compact object

Using the optical reference geometry approach, we have derived a general expression for the ellipticity of a slowly rotating fluid configuration using a Newtonian force balance equation in the conformally projected absolute 3-space, in the realm of general relativity. Further, with the help of the Hartle - Thorne (H - T) metric for a slowly rotating compact object, we have evaluated the centrifugal force acting on a fluid element and also evaluated the ellipticity and found that the centrifugal reversal occurs at around , and the ellipticity maximum at around . The result has been compared with that of Chandrasekhar and Miller which was obtained in the full 4-spacetime formalism.