conformal mapping philosophy fish and curved space

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. Then, it briefly sets forth the underlying idea of a general relativity-like spacetime. This non-technical explanation first defines the terms used in the introductory material of this entry. 5 An overview of AdS spacetime in physics and its properties.2.1 Closed timelike curves and the universal cover.1.5 De Sitter space and anti-de Sitter space viewed as embedded in five dimensions.1.4 Anti-de Sitter space distinguished from de Sitter space.1.3 De Sitter space in general relativity.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 (non-compact) dimension. As such, they are exact solutions of Einstein's field equations for an empty universe with a positive, zero, or negative cosmological constant, respectively.Īnti-de Sitter space generalises to any number of space dimensions. The cases of spacetime of constant curvature are de Sitter space (positive), Minkowski space (zero), and anti-de Sitter space (negative). 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.Įinstein'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. Willem de Sitter and Albert Einstein worked together closely in Leiden in the 1920s on the spacetime structure of the universe. 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.

In mathematics and physics, n-dimensional anti-de Sitter space (AdS n) is a maximally symmetric Lorentzian manifold with constant negative scalar curvature. ( June 2016) ( Learn how and when to remove this template message) Please help to improve this article by introducing more precise citations. This article includes a list of references, related reading or external links, but its sources remain unclear because it lacks inline citations.

Conformal mapping philosophy fish and curved space