On the mass of a uniform density star in higher dimensions

Abstract

Within the framework of higher dimensions the mass of a uniform density star is evaluated. The four-dimensional upper bound for the mass-to-radius ratio obtained by Schwarzschild is generalized within the framework of higher- dimensional spacetime. It is found that the analogue upper bound for the mass- to-radius ratio in higher dimensions tends to increase at first as the number of dimensions of spacetime increases, it attains amaximumat nine dimensions and thereafter decreases. It is found that D = 4 is the lowest number of spacetime dimensions for which the mass-to-radius ratio of a uniform density star can be derived.