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

A curved ‘two-dimensional’ absolute intrinsic metric spacetime(∅^�;∅^cs∅^t)on the vertical intrinsicspacetime hyperplane; its invariantly projected flat ‘two-dimensional’ absolute proper intrinsicmetric spacetime(∅�′ab;∅csab∅t′ab)and a flat ‘two-dimensional’ absolute proper metric spacetime(�′ab;csabt′ab), as the outward manifestation of the latter, evolve from a flat ‘four-dimensional’absolute metric spacetime(I^E3;^cs^t)and its underlying flat ‘two-dimensional’ absolute intrinsicmetric spacetime(∅^�;∅^cs∅^t), in all finite neighborhood of the source of a long-range metric forcefield. The flat four-dimensional relative proper metric spacetime(IE′3;cst′)and its underlying flattwo-dimensional relative proper intrinsic metric spacetime(∅�′;∅cs∅t′), remain unchanged withinthe field. The geometry is valid with respect to 3-observers located in the relative proper Euclidean3-spaceIE′3.A pair of absolute intrinsic metric tensor equations derived on the curved(∅^�;∅^cs∅^t)are solvedalgebraically to obtain the absolute intrinsic metric tensor and absolute intrinsic Ricci tensor on thecurved(∅^�;∅^cs∅^t)in terms of an isolated absolute intrinsic geometrical parameter, referred to asabsolute intrinsic ‘static flow’ speed, which the source of a long-range absolute intrinsic metric forcefield causes to be established on the extended curved(∅^�;∅^cs∅^t)from its location. This thirdpart of this paper is the conclusion of the development of absolute intrinsic Riemann geometry onthe curved ‘two-dimensional’(∅^�;∅^cs∅^t)at the first stage of evolutions of spacetime and intrinsicspacetime in long-range metric force fields, started in the first and second parts. The first stageshows up as a numerical evolution. Extension to the second stage shall be done in the fourth andfinal part of this paper. Particularization to the gravitational field shall then follow in another article.