## Evolutionary Sequence of Spacetime/intrinsic Spacetime and Associated Sequence of Geometries in a Metric Force Field. Part I.

**Authors:** Akindele J. Adekugbe

Having isolated a four-world picture in which four symmetrical universes in different
spacetime domains coexist and in which an isolated two-dimensional intrinsic spacetime
underlies the four-dimensional spacetime in each universe, and having shown that
the special theory of relativity rests on a four-world background elsewhere, we review
the geometry of spacetime/intrinsic spacetime in a long-range metric force field within
the four-world picture in the four parts of this paper. We show within an elaborate programme
that the four-dimensional metric spacetime and its underlying two-dimensional
intrinsic metric spacetime undergo two stages of evolution in the sequence of absolute
spacetime/absolute intrinsic spacetime → proper spacetime/proper intrinsic spacetime → relativistic spacetime/relativistic intrinsic spacetime in all finite neighborhood of
a long-range metric force field and that these are supported by a sequence of spacetime
/intrinic spacetime geometries. The programme takes off in this first paper by
isolating two classes of three-dimensional Riemannian metric space namely, the conventional
three-dimensional Riemannian metric space and a new 'three-dimensional'
absolute intrinsic Riemannian metric space.

**Comments:** 11 pages. Submitted to Progress in Physics

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### Submission history

[v1] 30 Nov 2010

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