The clash between de Sitter and anti-de Sitter space

TL;DR

This paper explores the theoretical possibility of solutions in Einstein gravity that transition between de Sitter and anti-de Sitter spaces, establishing a no-go theorem under reasonable matter conditions and discussing holographic implications.

Contribution

It proves a no-go theorem for such solutions with reasonable matter and discusses potential holographic interpretations of solutions that violate energy conditions.

Findings

No-go theorem for solutions with reasonable matter

Existence of solutions violating energy conditions

Discussion of holographic dualities

Abstract

We investigate solutions that are dynamically evolving between asymptotically de Sitter and asymptotically anti-de Sitter regions in the context of Einstein gravity coupled to general matter fields in d dimensions. We demonstrate the existence of a no go theorem whenever the matter content of the theory is 'reasonable', i.e. such that the weak energy condition is satisfied. We show that there exist solutions for which the energy conditions are violated in a finite region of the spacetime. We speculate on the holographic interpretation of these gravitational backgrounds by combining ideas from the AdS/CFT and the dS/CFT dualities.