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Contents

Definition

Up to isometry, the anti de Sitter spacetime of dimension $d + 1$ is the pseudo-Riemannian manifold whose underlying manifold is the submanifold of the Cartesian space $\mathbb{R}^{d+2}$ that solves the equation

and equipped with the metric induced from the ambient metric

where $x^i\colon \mathbb{R}^{d+2} \to \mathbb{R}$ denote the canonical coordinates on a Cartesian space.

Properties

Conformal boundary

(…)

Holography

Asymptotically ant-de Sitter spaces play a central role in the realization of the holographic principle by AdS/CFT correspondence.

Related concepts

• anti de Sitter group

• de Sitter spacetime

• super anti de Sitter spacetime

• near-horizon geometry

References

• Ingemar Bengtsson, Anti-de Sitter space lecture notes (pdf)

• Leonardo Castellani, Riccardo D'Auria, Pietro Fré, volume 1, chapter I.3.8 of Supergravity and Superstrings - A Geometric Perspective, World Scientific (1991)

• C. Frances, The conformal boundary of anti-de Sitter space-times, in AdS/CFT correspondence: Einstein metrics and their conformal boundaries , 205–216, IRMA Lect. Math. Theor. Phys., 8, Eur. Math. Soc., Zürich, 2005 (pdf)

• Gary Gibbons, Anti-de-Sitter spacetime and its uses (arXiv:1110.1206)

• Wikipedia (English): anti de Sitter space

• Abdelghani Zeghib, On closed anti de Sitter spacetimes, Math. Ann. 310, 695–716 (1998) (pdf)