Anti-de Sitter space | Wikipedia audio article
Channel: wikipedia tts
Date: 2018-12-28

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Anti-de_Sitter_space


00:01:48 1 Non-technical explanation
00:02:48 1.1 Technical terms translated
00:03:51 1.2 Spacetime in general relativity
00:04:15 1.3 de Sitter space in general relativity
00:07:17 1.4 Anti-de Sitter space distinguished from de Sitter space
00:08:04 1.5 de Sitter space and anti-de Sitter space viewed as embedded in five dimensions
00:08:58 1.6 Caveats
00:10:03 2 Definition and properties
00:11:32 2.1 Closed timelike curves and the universal cover
00:14:57 2.2 Symmetries
00:15:06 3 Coordinate patches
00:16:09 4 As a homogeneous, symmetric space
00:16:42 5 A mathematical definition for anti-de Sitter space and its properties
00:16:51 5.1 Global coordinates
00:17:18 5.2 Poincaré coordinates
00:22:23 5.3 Geometric properties
00:27:14 6 References
00:30:09 7 External links
00:38:45 Poincaré coordinates
00:45:47 Geometric properties



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SUMMARY
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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.