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arXiv · hep-th/0209156

Notes on Euclidean de Sitter space

V. Suneeta
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Abstract

We discuss issues relating to the topology of Euclidean de Sitter space. We show that in (2+1) dimensions, the Euclidean continuation of the`causal diamond', i.e the region of spacetime accessible to a timelike observer, is a three-hemisphere. However, when de Sitter entropy is computed in a `stretched horizon' picture, then we argue that the correct Euclidean topology is a solid torus. The solid torus shrinks and degenerates into a three-hemisphere as one goes from the `stretched horizon' to the horizon, giving the Euclidean continuation of the causal diamond. We finally comment on the generalisation of these results to higher dimensions.

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V. Suneeta. 2002-10-16. Notes on Euclidean de Sitter space. https://doi.org/10.1088/1126-6708%2F2002%2F09%2F040

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