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H. Dicke, Phys. Rev. 125, 2163 (1962).  J. Isenberg and J. Nester, Canonical Gravity, in General Relativity and Gravitation, Vol. I, Editor A. Held, Plenum Press (1980).  L. Parker, Particle Creation by the Expansion of the Universe, in Handbook of Astronomy, Astrophysics and Geophysics, Vol. G. Elmegreen, Gordon & Breach (1988).  D. Østvang, chapter 3 of this thesis (2001).  D. Østvang, chapter 4 of this thesis (2001).  D. Østvang, chapter 5 of this thesis (2001). 42 Chapter Two: On the Non-Kinematical Evolution of the 3-Geometry 43 44 On the Non-Kinematical Evolution of the 3-Geometry by Dag Østvang Institutt for fysikk, Norges teknisk-naturvitenskapelige universitet, NTNU N-7491 Trondheim, Norway Abstract We introduce the “quasi-metric” framework consisting of a 4-dimensional differential space-time manifold equipped with a one-parameter family of Lorentzian 4-metrics parameterized by a global time function.
In this section we will see ⋆ that we in fact have a=at . 39 In the following it is convenient to introduce the difference in coordinate 3-velocity between an arbitrary test particle and the local FO. We call this quantity wt , and we write its square as w 2 . Thus we define (using a GTCS) j w(t) ≡ t0 N j dxj + c, dτF t N ⋆ dτF i γ≡(1 − c−2 w(t) , w(t)i )−1/2 = dτt (45) where τt is the proper time as measured along the curve. Note that wt is an object intrinsic to the FHSs and that we may separate out the t-dependence of wt , namely  w(t)j = t t w(t0 )j ≡ wj , t0 t0 j w(t) = t0 j t0 w(t0 ) ≡ w j .
It is not yet clear whether or not this theory is viable. However, it does agree with the classic solar system tests. 1 Introduction The class of space-time theories defined as metric theories of gravity satisfies the following postulates : (1) space-time is equipped with a Lorentzian non-degenerate metric, (2) inertial test particles follow non-spacelike geodesics of this metric, and (3) in the local Lorentz frames of the metric, the non-gravitational physics is as in special relativity. In light of the highly successful record of the metric framework, and with the lack of any obvious experimental motivation, one might wonder why anyone should bother to construct a non-metric alternative.
Advances in Natural Language Procg. [comp sci, AI] by J. Vicedo, et. al.,