Using the geodesic method, what is an expression for the light path, and the falling path of a mass, or at least the vertical (x) position of each as a function of time, with the light initially horizontal? The "a" is the field acceleration. If results are interesting, a pedagogical paper may be considered.
ds2=-(1-ax/c2)2c2dt2 + (1-ax/c2)-2dx2 + dy2 + dz2
What do you think constrains the light to a sheet? Feynman suggested that light takes all possible paths, not only the conventional straight line of travel and the assumption of equal angles of incidence and reflection.
Frank, I did not place any constraint on the light path. The material sheet is a configuration of matter that produces a uniform gravitational field. We can just stop the light when it gets to the sheet, like it would stop if it reached the Earth, etc. The question is to find the light path by the geodesic method.
I have a new short paper which I claim is on a high school level which illustrates the separate effects of time dilation and spatial distortion due to gravity on the path of light. See link.
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