Abstract
In this paper, we investigate the conditions for a (non-)regular perfect fluid with a cosmological constant in hydrostatic equilibrium for d-dimensional spacetime. The generalized Tolman–Oppenheimer–Volkoff equation is derived and a bound for the cosmological constant is given for the various geometries. We also follow Buchdahl's method to get a bound for the degree of compactification and show that it is valid only for regular spherical topology solutions, and for d = 3 toroidal/planar topology solutions. We also study the regions where the toroidal/planar topology solution in d = 3 is in hydrostatic equilibrium.
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