Redshift and the Rotating Gravitational Field

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Previously it was shown that if a weak gravitational field is modeled as a background of oscillating gravitons described by normal coordinates, then the field naturally exhibits rotational kinetic energy. The conformal metric associated with this oscillatory motion is given by gμν = eiωt ημν, and the corresponding energy momentum tensor by Tμν = frac12 Iω2 ημν. In this paper the metric is extended to include constant radiant energy thereby amending the spacetime metric to: gμν = ei(ω+ρ)t ημν. The energy momentum tensor then becomes: Tμν = [frac12 Iω2 + (3c2/16G)(ρ2 + 2nωρ)]. Analyzing this energy equation at the microscopic level, where energies are assumed to become discrete, it is found a photon of frequency ν0 traversing through a rotating gravitational field (having frequency νg) becomes coupled to the field and redshifted by the amount ν' = ν0 - r (ν0 νg)1/2.