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In mathematics and physics, ''n''-dimensional anti-de Sitter space (AdS''n'') is a maximally symmetric Lorentzian manifold with constant negative scalar curvature. It is the Lorentzian analogue of hyperbolic space, just as Minkowski space is the analogues of Euclidean space and de Sitter space is the analogue of elliptical space. It is best known for its role in the AdS/CFT correspondence. The 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 the 1920s in Leiden on the spacetime structure of the universe. In the language of general relativity, anti-de Sitter space is a maximally symmetric vacuum solution of Einstein's field equation with a negative (attractive) cosmological constant , corresponding to a negative energy density and positive pressure of the vacuum. In mathematics, anti-de Sitter space is sometimes defined more generally as a space of arbitrary metric signature . In physics, often only the case of one timelike dimension is considered. This corresponds to the equivalent metric signatures and , where the choice is by a sign convention. ==Non-technical explanation== This non-technical explanation first defines the terms used in the introductory material of this entry. Then, it briefly sets forth the underlying idea of a general relativity-like spacetime. Then it discusses how de Sitter space describes a distinct variant of the ordinary spacetime of general relativity (called Minkowski space) related to the cosmological constant, and how anti-de Sitter space differs from de Sitter space. It also explains that Minkowski space, de Sitter space and anti-de Sitter space, as applied to general relativity, can all be thought of as being embedded in a flat five-dimensional spacetime. Finally, it offers some caveats that describe in general terms how this non-technical explanation fails to capture the full detail of the mathematical concept. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Anti-de Sitter space」の詳細全文を読む スポンサード リンク
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