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# curvature of spacetime

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A property of spacetime in which the familiar laws of geometry no longer apply in regions where gravitational fields are strong. In general relativity the geometry of spacetime is intimately connected with the distribution of matter. In a space of only two dimensions, such as a flat rubber sheet, Euclidean geometry applies so that the sum of the internal angles of a triangle on the sheet is 180°. If a massive object is placed on the rubber sheet, the sheet will distort and the paths of objects moving on the sheet will become curved. This is, in essence, what happens in general relativity.

The Universe as a whole may have positive, negative, or zero curvature. A universe with positive curvature would curve back on itself like the surface of a sphere so that one could in principle travel out into space and eventually end back at the same place. Such a universe is a closed universe, having finite size. A universe with negative curvature, however, would be an open universe, infinite in size.

The curvature of space can be measured with geometric tests. On the surface of a sphere, which has positive curvature, the sum of the angles in a triangle is greater than 180°; on the surface of a saddle, which has negative curvature, the sum of the angles is less than 180°. Observations of the cosmic background radiation provide such a geometric test, with the surprising result that the Universe has zero curvature (see cosmology). In other words, it is spatially flat (Euclidean) and infinite in both space and time. One possible explanation is provided by the theory of the inflationary universe, which proposes that the Universe expanded extremely quickly shortly after the Big Bang. If inflationary theory is true, our entire observable Universe, over 10 billion light years in size, may be only a speck within the greater Universe—and this may explain why we fail to see any curvature. Returning to the analogy of the surface of a sphere, if the triangle on the sphere is small compared with the size of the sphere, the sum of the angles in a triangle will not differ significantly from 180°. If the theory of inflation is correct, the Universe may actually have positive or negative curvature, but we see too small a part of it to detect the curvature.

Subjects: Astronomy and Astrophysics.

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