Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-02-25
Adv.Theor.Math.Phys. 6 (2003) 307-327
Physics
High Energy Physics
High Energy Physics - Theory
16 pages, Latex2e, v2: reference corrected, v3: reference added, material added to the introduction
Scientific paper
Motivated by recent proposals for a de Sitter version of the AdS/CFT correspondence, we give some topological restrictions on spacetimes of de Sitter type, i.e., spacetimes with $\Lambda>0$, which admit a regular past and/or future conformal boundary. For example we show that if $M^{n+1}$, $n \ge 2$, is a globally hyperbolic spacetime obeying suitable energy conditions, which is of de Sitter type, with a conformal boundary to both the past and future, then if one of these boundaries is compact, it must have finite fundamental group and its conformal class must contain a metric of positive scalar curvature. Our results are closely related to theorems of Witten and Yau hep-th/9910245 pertaining to the Euclidean formulation of the AdS/CFT correspondence.
Andersson L.-L.
Galloway Gregory J.
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