Redshift and the Rotating Gravitational Field

Abstract

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 g{\mu}{\nu} = ei{\omega}t {\eta}{\mu}{\nu}, and the corresponding energy momentum tensor by T{\mu}{\nu} = $frac{1}{2}$ I{\omega}2 {\eta}{\mu}{\nu}. In this paper the metric is extended to include constant radiant energy thereby amending the spacetime metric to: g{\mu}{\nu} = ei({\omega}+{\rho})t {\eta}{\mu}{\nu}. The energy momentum tensor then becomes: T{\mu}{\nu} = [$frac{1}{2}$ I{\omega}2 + (3c2/16G)({\rho}2 + 2n{\omega}{\rho})]. Analyzing this energy equation at the microscopic level, where energies are assumed to become discrete, it is found a photon of frequency {\nu}0 traversing through a rotating gravitational field (having frequency {\nu}g) becomes coupled to the field and redshifted by the amount {\nu}' = {\nu}0 - r ({\nu}0 {\nu}g)1/2.