RELATIVISTIC STAR SOLUTIONS IN HIGHER DIMENSIONS

Abstract

A class of relativistic solutions of compact star which is in hydrostatic equilibrium is obtained in higher dimensions assuming a spherically symmetric space–time. The space–time geometry is assumed to be a (D-1)-spheroid immersed in a D-dimensional Euclidean space. It is noted that the parameter a which is the measure of spheroidicity of the space–time plays here an important role in determining the equation of state of the matter content in such a star. One obtains a realistic solution when the parameter a picks up values [Formula: see text] for D<9 and [Formula: see text] for space–time dimensions D≥9. It is also observed that the higher dimensional space–time accommodates a more massive compact object for a given size compared to that in the usual four dimensional space–times.