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

O. Akindele Adekugbe Joseph *

Department of Physics, Ondo State University of Science and Technology, Center for the Fundamental Theory and Unification, Okitipupa, Nigeria.

*Author to whom correspondence should be addressed.


Abstract

The flat two-dimensional relative proper intrinsic metric spacetime (\(\varnothing \rho^{\prime}, \varnothing c_s \varnothing t^{\prime}\)) underlying the flat four-dimensional relative proper metric spacetime \(\left(\mathbb{E}^{\prime 3}, c_s t^{\prime}\right)\), which emerges at the first stage of evolution of metric spacetime and intrinsic metric spacetime in long-range metric force fields, isolated in the first three parts of this paper, endures for no moment before transforming into a curved two-dimensional relative proper intrinsic metric spacetime with pseudo-orthogonal curvilinear intrinsic dimensions, (\(\varnothing \rho^{\prime}\) and \(\varnothing c_s \varnothing t^{\prime}\)), on the vertical intrinsic metric spacetime hyperplane, on the larger spacetime and intrinsic spacetime of combined positive (or our) universe and the negative universe. It therefore possesses intrinsic Lorentzian metric tensor at every point. It projects an underlying flat relativistic intrinsic metric spacetime \(\left(\varnothing \rho, \varnothing c_s \varnothing t\right)\), which is made manifested outwardly in a flat four-dimensional relativistic metric spacetime \(\left(\mathbb{E}^3, c_s t\right)\), at the second (and final) stage of evolution of metric spacetime and intrinsic metric spacetime in long-range metric force fields. The conclusion that the four-dimensional metric spacetime is everywhere flat in every Iong-range metric force field is reached.
The curved 'two-dimensional' absolute intrinsic metric spacetime (\(\varnothing \hat{\rho}, \varnothing \hat{c}_s \varnothing \hat{t}\)) with absolute intrinsic sub-Riemannian metric tensor \(\varnothing \hat{g}_{i k}\), which evolves at the first stage is brought forward to the second stage. The basic aspects of the theory of relativity on the flat relativistic metric spacetime, intrinsic theory of relativity on the underlying flat relativistic intrinsic metric spacetime and absolute intrinsic metric theory on the curved absolute intrinsic metric spacetime, associated with the presence of a metric force field in spacetime and intrinsic metric force field in intrinsic spacetime, are developed in terms of certain derived geometrical parameters, referred to as relative proper static flow speed, relative proper intrinsic static flow speed and absolute intrinsic static flow speed respectively. Particularization to the gravitational field will be a straight forward process, while using the results of this paper as template.

Keywords: Long-range metric force fields, second stage of evolution of spacetime and intrinsic spacetime, curved proper intrinsic metric spacetime, projective flat relativistic intrinsic metric spacetime, outward manifestation flat relativistic metric spacetime, static flowspeed


How to Cite

Joseph, O. A. A. (2022). Evolutionary Sequence of Spacetime and Intrinsic Spacetime and Associated Sequence of Geometries in Metric Force Fields IV. Physical Science International Journal, 26(5), 35–72. https://doi.org/10.9734/psij/2022/v26i5745

Downloads

Download data is not yet available.

References

Joseph OAA. Evolutionary sequence of spacetime/intrinsic spacetime and associated sequence of geometries in metric force fields I. Physical Science International Journal. 2021; 25(10):1-20. Available:https://doi.org/10.9734/psij/2021/ v25i1030284.

Joseph OAA. Evolutionary sequence of spacetime/intrinsic spacetime and associated sequence of geometries in metric force fields II. Physical Science International Journal. 2021;25(10):39-77. Available:https://doi.org/10.9734/psij/2021/ v25i1030287

Joseph OAA. Evolutionary sequence of spacetime/intrinsic spacetime and associated sequence of geometries in a metric force field III. Physical Science International Journal. 25(10):78-112. Available at: https://doi.org/10.9734/psij/2021/ v25i1030288.

Einstein A. The Principle of Relativity. (London: Methuen; reprints by Dover Publications); 1923.

Joseph OAA. Reformulating special relativity on a two-world background. Physical Science International Journal. 2020;24(8):44-87. Available:https://doi.org/10.9734/psij/2020/ v24i830209

Joseph OAA. Reformulating special relativity on a two-world background II. Physical Science International Journal. 2020;24(9):34-67. Available:https://doi.org/10.9734/psij/2020/ v24i930215

Joseph OAA. Re-interpretation of the two- world background of special relativity as four-world background I. Physical Science International Journal. 2020;24(12):10-38. Available:https://doi.org/10.9734/psij/2020/ v24i1230229

Joseph OAA. Re-interpretation of the two- world background of special relativity as four-world background II. 2021;25(2):37-57. Available:https://doi.org/10.9734/psij/2021/ v25i230243