In mathematics and physics, a de Sitter space is the analog in Minkowski space, or spacetime, of a sphere in ordinary, Euclidean space. The n-dimensional de Sitter space, denoted, is the Lorentzian manifold analog of an n-sphere (with its canonical Riemannian metric); it is maximally symmetric, has constant positive curvature, and is simply-connected for n at least 3.
In the language of general relativity, de Sitter space is the maximally symmetric, vacuum solution of Einstein's field equations with a positive (repulsive) cosmological constant (corresponding to a positive vacuum energy density and negative pressure). When n = 4 (3 space dimensions plus time), it is a cosmological model for the physical universe; see de Sitter universe.
De Sitter space was discovered by Willem de Sitter, and, at the same time, independently by Tullio Levi-Civita.
More recently it has been considered as the setting for special relativity rather than using Minkowski space. This formulation is called de Sitter relativity.
Read more about De Sitter Space: Definition, Properties, Static Coordinates, Flat Slicing, Open Slicing, Closed Slicing, DS Slicing
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