Variability of the Speed of Light in a Weak Gravitational Field

Bevelacqua Resources, 7531 Flint Crossing Circle SE, Owens Cross Roads, AL 35763 USA bevelresou@aol.com General relativity suggests that the speed of light is influence by the gravitational potential. Using the Schwarzschild metric, a previous paper noted that the influence of gravity on the speed of light could occur most strongly in the vicinity of a massive object (e.g., in the vicinity of a black hole). No temporal dependence was noted for the time-independent Schwarzschild metric. This paper evaluates the variability of the speed of light in a weak gravitational field. The solution of the resulting weak gravity field equations results in plane waves for the two polarization components of the gravitational wave. These solutions suggest that the speed of light varies with respect to time with a magnitude that is proportional to the polarization amplitude. Since this amplitude is very small, the effect on the speed of light is likely not measurable given current technology.