I think I heard long ago that the redshift of all parts of the surface of a spinning star as seen from a distant point on the axis is expected to be the same, at least in theory, because of the following argument. Please can anyone confirm or refute this? A body which is capable of being shaped by its own gravity forms a shape such that locally the surface is "level" or "equipotential" as seen by a local observer. The "potential" for this purpose is a combination of the effect of gravity and the effective potential for the centripetal acceleration caused by the rotation. This means that clocks run at the same rate at different locations on the surface, as seen locally, so clocks over the whole surface can be synchronized. This means that as seen from a distant position on the axis, the clocks rates are also synchronized, and similarly that the redshift of any processes at the surface is also the same. From the distant point of view, this is because the Special Relativity velocity time dilation for points further from the axis is exactly balanced by being at a higher gravitational potential. Is this correct? It seems plausible to me, but I'd like a second opinion.