The purpose of this article is to study the geometry of static space-times. We show that the energy density and pressure vanish on the boundary of a perfect fluid space-time, provided that it satisfies a suitable condition. Moreover, we provide an upper bound volume growth for geodesic balls of the base of static vacuum space similar to a classical result due to Bishop. In addition, we derive a weak version of the maximum principle of Omori-Yau at infinity for such spaces.
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