Particularization of the Sequence of Spacetime/Intrinsic Spacetime Geometries and Associated Sequence of Theories in Metric Force Fields in the Four-world Picture to the Gravitational Field I

Abstract

The two stages of evolutions of metric spacetime and intrinsic metric spacetime and the associated spacetime/intrinsic spacetime geometries in long range metric force fields, derived in the four-world picture in previous articles, are particularized to the gravitational field. The theory of relativity on flat four-dimensional gravitational-relativistic metric spacetime \((\mathbb{E}^3, c_s t\)) and the theory of intrinsic relativity on the underlying flat two-dimensional gravitational-relativistic intrinsic metric spacetime \((\varnothing \rho, \varnothing c_s \varnothing t\)), due to the presence of a long range metric force field in spacetime, as well as the absolute intrinsic metric theory (of the metric force field) on the curved 'two-dimensional' absolute intrinsic metric spacetime \((\varnothing \hat{\rho}, \varnothing \hat{c}_s \varnothing \hat{t}\)) with absolute intrinsic metric tensor \(\varnothing \hat{g}_{i k}\), all of which evolve at two stages of evolutions of metric spacetimes and intrinsic metric spacetimes in long range metric force fields in general, developed in the previous articles, are adapted to the gravitational field. They become the theory of gravitational relativity (TGR) on the flat four-dimensional relativistic metric spacetime, the theory of intrinsic gravitational relativity (TøGR) on the underlying flat two-dimensional relativistic intrinsic metric spacetime and the metric theory of absolute intrinsic gravity (MA \(\varnothing\) G) on the curved 'two-dimensional' absolute intrinsic metric spacetime, which evolve at two stages of evolutions of metric spacetime and intrinsic metric spacetime in a gravitational field of arbitrary strength. The basic aspects of these coexisting theories in the gravitational field are developed.