This question is inspired by this question about timekeeping.
I understand the geoid to be the surface matching the shape that the water on Earth's crust would take
- Under the effect of Earth's gravity
- under the effect of Earth's rotation
- If shallow channels were cut through Earth's landmasses (so that the shape could be estimated even in regions where land is present)
- Ignoring the effects of winds and tides
Is the geoid ALSO a surface of constant gravitational redshift? I think if there was no rotation in the problem it would be obvious that, yes, this is a surface of constant redshift. Is that still the case when there is "bulging" at the equator due to centrifugal forces?
