Abstract
In a spherically symmetric spacetime we find the general solution for a relativistic star in hydrostatic equilibrium having the spheroidal geometry for the 3-space embedded in 4-Euclidean space. The parameter is the measure of spheroidal character and determines the physical properties of the star. It has a lower bound ; stars with smaller mass to radius ratio can occur for all allowed while ultracompact stars, having ratios between 1/3 and 1/2, will have . It turns out that a wide range of values of can represent objects with the fluid density of a neutron star. The model is shown to possess all the desirable physical features.
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