Notes on Euclidean de Sitter space

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.

10 pages, 2 figures, LaTeX, reference added

References in corpus (8)

• The dS/CFT Correspondence
• Mass, Entropy and Holography in Asymptotically de Sitter Spaces
• Logarithmic correction to the Bekenstein-Hawking entropy of the BTZ black hole
• Some Aspects of the de Sitter/CFT Correspondence
• Conformal anomaly from dS/CFT correspondence
• Entropy of the three dimensional Schwarzschild-de Sitter black hole
• de Sitter entropy from conformal field theory
• Quantum Gravity on $d{S}_3$

Cited by in corpus (3)

• $T\bar{T}+{\Lambda }_2$ Deformed CFT on the Stretched dS${}_3$ Horizon
• Holographic networks for (1+1)-dimensional de Sitter spacetime
• Bubble Universe from Flat Spaces