General relativistic fluid spheres with nonzero vacuum energy density

Abstract

Bounds are developed for the ratios M/R and m/R for fluid spheres in asymptotically de Sitter or anti-de Sitter space-times, where M is the mass of the fluid sphere, and m is the total mass interior to R: M plus the interior vacuum energy. This represents a generalization of the work of Buchdahl to the case of a nonvanishing vacuum energy density. In the asymptotically de Sitter case, it is possible to construct models which have m/r→ 1/2 . Further, it is shown that static fluid spheres can exist in an asymptotically de Sitter space with vacuum energy density ρv only if their radius satisfies R≤(8πρv)1/2, a maximum radius smaller by a factor of 3−1/2 than the horizon size of the de Sitter space in the absence of a fluid sphere. If the vacuum energy density is negative, then the ratio m/R is shown to be bounded above by the asymptotically flat limit of (4)/(9), and the radius of a positive total mass (m) sphere is shown to be bounded above by R<(2π‖ρv‖)−1/2.