Not a homework assignment

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.