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anti de Sitter spacetime

Contents

Definition

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

i=1 d+1(x i) 2(x d+2) 2=0 \sum_{i = 1}^{d+1} (x^i)^2 - (x^{d+2})^2 = 0

and equipped with the metric induced from the ambient metric

g= i=1 d+1dx idx idx i+1dx i+t, g = \sum_{i = 1}^{d+1} d x^i \otimes d x^i - d x^{i+1} \otimes d x^{i+t} \,,

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

Properties

Conformal boundary

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Holography

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

References

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

  • 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

Revised on January 6, 2012 16:35:03 by Urs Schreiber (89.204.137.240)