Notes on Euclidean de Sitter space
High Energy Physics - Theory
2009-11-07 v2 General Relativity and Quantum Cosmology
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.
Cite
@article{arxiv.hep-th/0209156,
title = {Notes on Euclidean de Sitter space},
author = {V. Suneeta},
journal= {arXiv preprint arXiv:hep-th/0209156},
year = {2009}
}
Comments
10 pages, 2 figures, LaTeX, reference added