Buchdahl limit for d-dimensional spherical solutions with a cosmological constant

We investigate the conditions for which a d-dimensional perfect fluid solution is in hydrostatic equilibrium with a cosmological constant. We find a generalization of Buchdahl inequality and obtain an upper bound for the degree of compactification. Using the Tolman–Oppenheimer–Volkoff equation to get a lower bound for the degree of compactification we analyse the regions where the solution is in hydrostatic equilibrium. We obtain the inner metric solution and the pressure for the constant fluid density model.