Geometry of (Anti-)De Sitter space-time

Abstract

This work is an introduction to the De Sitter and Anti-de Sitter spacetimes, as the maximally symmetric constant curvature spacetimes with positive and negative Ricci curvature scalar R. We discuss their causal properties and the characterization of their geodesics, and look at the spaces embedded in flat Rp;q spacetimes with an additional dimension. We conclude that the geodesics in these spaces can be regarded as intersections with planes going through the origin of the embedding space, and comment on the consequences