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## Main Question or Discussion Point

Consider a theoretical nonrotating solid massive ball of constant density. A shaft is drilled from a point on the surface down to the center. A light source on the surface is aimed down the shaft. Observers at each end of the shaft carry clocks which initially were synchronized before separation.

1. The gravitational potential (or spacetime curvature) at the exact center of the sphere is zero, as calculated by the shell theorem, etc.

2. The clock at the surface will become time-dilated (i.e., the clock runs slower) compared to the clock at the center. For this reason, the spectrum of the light beam from the surface will appear redshifted when viewed by the observer at the center.

3. The light beam descending from the surface to the center will experience gravitational acceleration toward the center of the sphere during its journey. Gravitational acceleration at any instant is linearly proportional to distance from the center (up to and including the surface). Due to this the gravitational acceleration, the light beam from the surface will appear to be blueshifted to the observer at the center.

I would like to confirm that each of the above 3 points is correct. Also, is there a single equation for calculating the net gravitational redshift/blueshift resulting from these two causes combined, or is it easiest just to calculate each separately and then offset them against each other?

1. The gravitational potential (or spacetime curvature) at the exact center of the sphere is zero, as calculated by the shell theorem, etc.

2. The clock at the surface will become time-dilated (i.e., the clock runs slower) compared to the clock at the center. For this reason, the spectrum of the light beam from the surface will appear redshifted when viewed by the observer at the center.

3. The light beam descending from the surface to the center will experience gravitational acceleration toward the center of the sphere during its journey. Gravitational acceleration at any instant is linearly proportional to distance from the center (up to and including the surface). Due to this the gravitational acceleration, the light beam from the surface will appear to be blueshifted to the observer at the center.

I would like to confirm that each of the above 3 points is correct. Also, is there a single equation for calculating the net gravitational redshift/blueshift resulting from these two causes combined, or is it easiest just to calculate each separately and then offset them against each other?