I have been wondering what to expect if there was a hole, from pole to pole, that inside which we could measure the Einstein red and blue shifts due to gravity. At first, I suspect a blue-shift as light travels from the surface of the Earth to the center; just less and less as the center is approached. But, and here is where I become ashamed even to have imagined...isn't this the same as light going from large gravity to smaller gravity? A red-shift in other words, like a photon leaving a massive body? All I believe for sure is that a photon would be restored to its original wavelength if it was measured at the poles.