The McVittie solution with a negative cosmological constant

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Whereas current cosmological observations suggest that the universe is dominated by a positive cosmological constant (Λ> 0), the AdS/CFT correspondence tells us that the case Λ<0 is still worthy of consideration. In this paper we study the McVittie solution with Λ<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 Λ<0 ensures collapse to a Big Crunch, a feature which completely dominates the global structure.