Anti-De Sitter Space

(Differential Geometry)

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Differential Geometry
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What is Anti-de Sitter space?

In mathematics and physics, n-dimensional anti-de Sitter space (AdSn) is a maximally symmetric Lorentzian manifold with constant negative scalar curvature. Anti-de Sitter space and de Sitter space are named after Willem de Sitter (1872–1934), professor of astronomy at Leiden University and director of the Leiden Observatory. Willem de Sitter and Albert Einstein worked together closely in Leiden in the 1920s on the spacetime structure of the universe. Manifolds of constant curvature are most familiar in the case of two dimensions, where the surface of a sphere is a surface of constant positive curvature, a flat (Euclidean) plane is a surface of constant zero curvature, and a hyperbolic plane is a surface of constant negative curvature. Einstein's general theory of relativity places space and time on equal footing, so that one considers the geometry of a unified spacetime instead of considering space and time separately. The cases of spacetime of constant curvature are de Sitter space (positive), Minkowski space (zero), and anti-de Sitter space (negative). As such, they are exact solutions of Einstein's field equations for an empty universe with a positive, zero, or negative cosmological constant, respectively. Anti-de Sitter space generalises to any number of space dimensions. In higher dimensions, it is best known for its role in the AdS/CFT correspondence, which suggests that it is possible to describe a force in quantum mechanics (like electromagnetism, the weak force or the strong force) in a certain number of dimensions (for example four) with a string theory where the strings exist in an anti-de Sitter space, with one additional dimension.

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differential geometryexact solutions in general relativitymixturesolutionsubstance

Synonyms

AdSAdS metricAdS spaceAdS3Anti de sitterAnti-de Sitter spacetime

Translations

Anti-de Sitter-metriek (nl)Anti-de-Sitter-Raum (de)Espace anti de Sitter (fr)Espacio anti de Sitter (es)Przestrzeń anty de Sittera (pl)Spazio Anti de Sitter (it)Антидеситтеровское пространство (ru)Антидесіттерівській простір (uk)반 더 시터르 공간 (ko)反ド・ジッター空間 (ja)反德西特空間 (zh)

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