The McVittie solution with a negative cosmological constant

Abstract

Whereas current cosmological observations suggest that the universe is dominated by a positive cosmological constant ($\Lambda >0$), the AdS/CFT correspondence tells us that the case $\Lambda <0$ is still worthy of consideration. In this paper we study the McVittie solution with $\Lambda <0$. Following a related study, the solution is understood here by way of a systematic construction of conformal diagrams based on detailed numerical integrations of the null geodesic equations. As in the pure Robertson - Walker case, we find that $\Lambda <0$ ensures collapse to a Big Crunch, a feature which completely dominates the global structure.

6 pages twocolumn revtex 4-1 8 figures updated references Final form to appear in Phys Rev D

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