Phys. Rev. D 66, 023003 (2002) [4 pages]Gravitational equilibrium in the presence of a positive cosmological constantReceived 2 April 2002; published 16 July 2002 We reconsider the virial theorem in the presence of a positive cosmological constant Λ. Assuming steady state, we derive an inequality of the form ρ>~A(Λ/8πGN) for the mean density ρ of the astrophysical object. The parameter A depends only on the shape of the object. With a minimum at Asphere=2, its value can increase by several orders of magnitude as the shape of the object deviates from a spherically symmetric one. This indicates that flattened matter distributions such as, e.g., clusters or superclusters, with low density, cannot be in gravitational equilibrium. © 2002 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevD.66.023003
DOI:
10.1103/PhysRevD.66.023003
PACS:
98.10.+z, 04.25.Nx, 98.20.-d, 98.35.Df
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