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

The flat two-dimensional relative proper intrinsic metric spacetime(∅ρ′,∅cs∅t′)underlying theflat four-dimensional relative proper metric spacetime(IE′3,cst′), which emerges at the firststage of evolution of metric spacetime and intrinsic metric spacetime in long-range metric forcefields, isolated in the first three parts of this paper, endures for no moment before transforminginto a curved two-dimensional relative proper intrinsic metric spacetime with pseudo-orthogonalcurvilinear intrinsic dimensions,∅ρ′and∅cs∅t′, on the vertical intrinsic metric spacetimehyperplane, on the larger spacetime and intrinsic spacetime of combined positive (or our) universeand the negative universe. It therefore possesses intrinsic Lorentzian metric tensor at every point.It projects an underlying flat relativistic intrinsic metric spacetime(∅ρ,∅cs∅t), which is mademanifested outwardly in a flat four-dimensional relativistic metric spacetime(IE3,cst), at the second(and final) stage of evolution of metric spacetime and intrinsic metric spacetime in long-range metricforce fields. The conclusion that the four-dimensional metric spacetime is everywhere flat in everylong-range metric force field is reached.The curved ‘two-dimensional’ absolute intrinsic metric spacetime(∅ˆρ,∅ˆcs∅ˆt)with absoluteintrinsic sub-Riemannian metric tensor∅ˆgik, which evolves at the first stage is brought forwardto the second stage. The basic aspects of the theory of relativity on the flat relativistic metricspacetime, intrinsic theory of relativity on the underlying flat relativistic intrinsic metric spacetimeand absolute intrinsic metric theory on the curved absolute intrinsic metric spacetime, associatedwith the presence of a metric force field in spacetime and intrinsic metric force field in intrinsicspacetime, are developed in terms of certain derived geometrical parameters, referred to asrelative proper static flow speed, relative proper intrinsic static flow speed and absolute intrinsicstatic flow speed respectively. Particularization to the gravitational field will be a straight forwardprocess, while using the results of this paper as template.