**Authors:** Akindele O. Adekugbe Joseph

An analytical approach to the theory of gravitational relativity (TGR) and combined theory of gravitational relativity and special theory of relativity (TGR+SR) on the flat spacetime of TGR in a gravitational field of arbitrary strength is developed to complement the graphical approach developed in the first part of this paper. The analytical approach to TGR bears an interesting analogy to the analytical approach to SR developed by Albert Einstein. Relations for (or transformations of) mass, force, energy, gravitational potential, gravitational field (or acceleration), gravitational velocity, frequency and other parameters, are derived on flat spacetime in the context of TGR. These are relations that incorporate the effect of gravitational relativity into the classical and special-relativistic values of parameters at every point on flat spacetime in a gravitational field of arbitrary strength. Local Lorentz invariance (LLI) is validated on the flat spacetime of TGR. The weak equivalence principle (WEP) is shown to be valid in the context of TGR as long as it is valid in classical gravitation. The modified (or gravitational-relativistic) form of the Newtonian gravitational force law on flat spacetime in the context of TGR is derived. The non-trivial relationships among the various mass concepts in physics namely, the inertial mass, the passive gravitational mass, the active gravitational mass and the rest mass, which the derived mass relation in the context of TGR implies, are highlighted and the elusive rest mass and classical radius of a gravitational field source are calculated from the observed (or inertial) mass and the observed radius of the field source. The exterior Schwarzschild line element in the general theory of relativity is shown to pertain to the measurable sub-space of TGR (which is a fictitious curved spacetime with sub-Riemannian metric tensor), whereas the total space of TGR is the observed flat spacetime with constant Lorentzian metric tensor.

**Comments:** 64 Pages. Article from volume one of The Fundamental Theory ... monograph series on an evolving fundamental theory of physics by the author.

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[v1] 2012-07-11 07:21:03

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