Mapping AdS to dS spaces and back

Understand

We derive a map between Einstein spaces of positive and negative curvature, including scalar matter.

• Starting from a space of positive curvature with some dimensions compactified on a sphere and analytically continuing the number of compact dimensions, we obtain a space of negative curvature with a compact hyperbolic subspace, and vice versa.
• Prime examples of such spaces are de Sitter (dS) and anti-de Sitter (AdS) space, as well as black hole spacetimes with (A)dS asymptotics and perturbed versions thereof, which play an important role in holography.
• This map extends work done by Caldarelli et al., who map asymptotically AdS spaces to Ricci-flat ones.