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2012

The McVittie solution with a negative cosmological constant

Landry, Philippe, Abdelqader, Majd, Lake, Kayll

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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.

The McVittie solution with a negative cosmological constant · Around

Built on

G. C. McVittie, Mon. Not. R. Astron. Soc. 93
1962
Earlier work this paper cites.
S. W. Hawking and G. F. R. Ellis, The large scale structure of space-time
1973
Earlier work this paper cites.
For a more general result see F. J. Tipler, Ap. J. 209
1976
Earlier work this paper cites.

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We use geometrical units and a signature of +2 throughout. Functional dependence is designated only on the first appearance of a function
Cited in the paper.
M ≡ ℛ θ ϕ θ ϕ R 3 / 2 M\equiv\mathcal{R}_{\theta\phi}^{\;\;\;\;\theta\phi}R^{3}/2 where ℛ \mathcal{R} is the Riemann tensor
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This package runs within Maple. The GRTensorII software and documentation is distributed freely from the address http://grtensor.org
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Then

See, for example, V. Faraoni, A. F. Zambrano Moreno and R. Nandra, Phys. Rev. D 85
Original
2010
Later among the works it cites.
K. Lake and M. Abdelqader, Phys. Rev. D 84
2011
Later among the works it cites.

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