BEHAVIOR OF THE CENTRIFUGAL FORCE AND OF ELLIPTICITY FOR A SLOWLY ROTATING FLUID CONFIGURATION WITH DIFFERENT EQUATIONS OF STATE

We have evaluated the centrifugal force acting on a fluid element and the ellipticity of the fluid configuration, which is slowly rotating, using the Hartle-Thorne solution for different equations of state. The centrifugal force shows a maximum in every case, whereas the reversal in sign could be seen in only one case and the system becomes unstabl e in other cases. The ellipticity as calculated from the usual definit ion shows maxima, whereas the definition obtained from the equilibrati on of the inertial forces, shows a negative behaviour, indicating that the system is prolate and not oblate. This prolate shape of the confi guration is similar to the one earlier found by Pfister and Braun for a rotating shell of matter, using the correct centrifugal force expres sion for the interior. The location of the centrifugal maxima gets fur ther away from the Schwarzschild radius (R-s) as the equation of state gets softer.