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Evolutionary Sequence of Spacetime and Intrinsic Spacetime and Associated Sequence of Geometries in Metric Force Fields I

  • O. Akindele Adekugbe Joseph

Physical Science International Journal, Page 1-20
DOI: 10.9734/psij/2021/v25i1030284
Published: 14 December 2021

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Abstract


Two classes of three-dimensional metric spaces are identified. They are the conventional three-dimensional metric space and a new ‘three-dimensional’ absolute intrinsic metric space. Whereas an initial flat conventional proper metric space IE′3 can transform into a curved three-dimensionalRiemannian metric space IM′3 without any of its dimension spanning the time dimension (or in the absence of the time dimension), in conventional Riemann geometry, an initial flat ‘three-dimensional’ absolute intrinsic metric space ∅IˆE3 (as a flat hyper-surface) along the horizontal, evolves into a curved ‘three-dimensional’ absolute intrinsic metric space ∅IˆM3, which is curved (as a curved hyper-surface) toward the absolute intrinsic metric time ‘dimension’ along the vertical, and it is identified as ‘three-dimensional’ absolute intrinsic Riemannian metric space. It invariantly projects a flat ‘three-dimensional’ absolute proper intrinsic metric space ∅IE′3ab along the horizontal, which is made manifested outwardly in flat ‘three-dimensional’ absolute proper metric space IE′3ab, overlying it, both as flat hyper-surfaces along the horizontal. The flat conventional three-dimensional relative proper metric space IE′3 and its underlying flat three-dimensional relative proper intrinsic metric space ∅IE′3 remain unchanged. The observers are located in IE′3. The projective ∅IE′3ab is imperceptibly embedded in ∅IE′3 and IE′3ab in IE′3. The corresponding absolute intrinsic metric time ‘dimension’ is not curved from its vertical position simultaneously with ‘three-dimensional’ absolute intrinsic metric space. The development of absolute intrinsic Riemannian geometry is commenced and the conclusion that the resulting geometry is more all-encompassing then the conventional Riemannian geometry on curved conventional metric space IM′3 only is reached.


Keywords:
  • Conventional metric space
  • Riemann geometry
  • absolute intrinsic metric space
  • absolute intrinsic Riemann geometry
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How to Cite

Joseph, O. A. A. (2021). Evolutionary Sequence of Spacetime and Intrinsic Spacetime and Associated Sequence of Geometries in Metric Force Fields I. Physical Science International Journal, 25(10), 1-20. https://doi.org/10.9734/psij/2021/v25i1030284
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References

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