In mathematics and physics, n-dimensional anti de Sitter space, sometimes written, is a maximally symmetric Lorentzian manifold with constant negative scalar curvature. It is the Lorentzian analogue of n-dimensional hyperbolic space, just as Minkowski space and de Sitter space are the analogues of Euclidean and elliptical spaces respectively.
It is best known for its role in the AdS/CFT correspondence.
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 vacuum energy density and positive pressure).
In mathematics, anti de Sitter space is sometimes defined more generally as a space of arbitrary signature (p,q). Generally in physics only the case of one timelike dimension is relevant. Because of differing sign conventions, this may correspond to a signature of either (n−1, 1) or (1, n−1).
Read more about Anti De Sitter Space: Non-technical Explanation of Anti De Sitter Space, Definition and Properties, Coordinate Patches, Anti De Sitter As Homogeneous and Symmetric Space
Famous quotes containing the word space:
“True spoiling is nothing to do with what a child owns or with amount of attention he gets. he can have the major part of your income, living space and attention and not be spoiled, or he can have very little and be spoiled. It is not what he gets that is at issue. It is how and why he gets it. Spoiling is to do with the family balance of power.”
—Penelope Leach (20th century)