A general relativity thought experiment considering time rates in different reference frames experiencing identical acceleration and no relative motion.

Suppose:

On a planet-sized, non-spinning, homogeneous sphere, floating freely in space, there’s a tall tower. On the tower are a laser, a clock synchronized to the laser (counting wave cycles and dividing by the laser's fixed frequency, f_{0}), & a light receiver that measures frequency of an incoming laser beam and runs a second clock (also counting f_{0} wave cycles per second). The laser and receiver are focused on an identical set of equipment located at the bottom of a vertical shaft, directly below the tower. And, the laser and detector at the bottom of the shaft are, likewise, focused on the detector and laser, respectively, on the tower.

The tower height and shaft depth are selected to have the same gravitational acceleration, g_{0}, which is less than the surface gravity.

Because both locations experience identical gravity, and are stationary with respect to each other, relativity requires that clocks in each location will run at the same rate.

Observations:

Because the light path from shaft bottom to tower top is up-hill all the way, light arriving at the tower from the shaft will have diminished frequency (and its clock will run slower) while light originating on the tower will be blue shifted, to higher frequency, by the time it arrives at the bottom of the shaft. Both sets of clocks will show time running faster on the tower than down in the shaft. The two beams follow identical, though opposite, fixed-length paths, so the constantly accumulating difference in the wave cycle counts can only be explained by a difference in time rate.

My conclusions:

While the force vectors in 3-space can be canceled out, the total field and consequent time dilation must only accumulate. In this model, the center of mass of such a sphere would only be a local minima in spacetime. Just because there’s no net gravity in one location doesn’t mean it's not uphill and/or downhill from other frames of reference, also of zero gravity.

I am guessing the time dilation at the center of the sphere will be that one would expect from a field proportional to the sphere's mass density multiplied by its radius... mass divided by distance squared.

Changes in potential energy require changes in time rate.

I would appreciate your thoughts.