Simple generalizations of Anti-de Sitter space-time

TL;DR

This paper introduces new cosmological solutions that extend Anti-de Sitter space-time by incorporating fluids with various equations of state, revealing deformed hyperboloids and altered Killing vector structures.

Contribution

It generalizes AdS solutions to include different fluid equations of state and analyzes their embedding and geometric properties.

Findings

Solutions can be embedded in flat 5D space-time.

Deformed hyperboloids represent the full manifolds.

Different Killing vector structures imply new horizon features.

Abstract

We consider new cosmological solutions which generalize the cosmological patch of the Anti-de Sitter (AdS) space-time, allowing for fluids with equations of state such that $w\neq -1$. We use them to derive the associated full manifolds. We find that these solutions can all be embedded in flat five-dimensional space-time with $--+++$ signature, revealing deformed hyperboloids. The topology and causal-structure of these spaces is therefore unchanged, and closed time-like curves are identified, before a covering space is considered. However the structure of Killing vector fields is entirely different and so we may expect a different structure of Killing horizons in these solutions.