Hydrostatic equilibrium of a perfect fluid sphere with exterior higher-dimensional Schwarzschild spacetime

We discuss the question of how the number of dimensions of space and time c an influence the equilibrium configurations of stars. We find that dimensio nality does increase the effect of mass but not the contribution of the pre ssure, which is the same in any dimension. In the presence of a (positive) cosmological constant the condition of hydrostatic equilibrium imposes a lo wer limit on mass and matter density. We show how this limit depends on the number of dimensions and suggest that Lambda > 0 is more effective in 4D t han in higher dimensions. We obtain a general limit for the degree of compa ctification (gravitational potential on the boundary) of perfect fluid star s in D dimensions. We argue that the effects of gravity are stronger in 4D than in any other number of dimensions. The generality of the results is al so discussed.