Is the Sagnac effect a reliable measure of rotation in Kerr space-time?

[PAllen]

But in the Gravity Probe B experiment the precession was measured relative to a distant star, under the assumption that without the Earth nearby there would be no precession relative to that distant star. How is this assumption justified?

W assume our universe is an FLRW solution. There is no reason for this to be true within GR as a theory. We pick boundary specific conditions such that the solution with those conditions matches observation. Unless the theory forces those boundary conditions, it provides no explanation of what is behind them. Einstein strongly hoped GR would not need arbitrary boundary conditions, and considered it major defect that it does. It is up to some future theory to provide an explanatory framework.

 

[WannabeNewton]

Is it just a coincidence that the local measurement of rotation (based on inertia, Sagnac) matches the global measurement of rotation (based on light from distant stars) ?

See post #3. To repeat, all of those fail to agree in Kerr space-time, which is a particular instance of what Bill elucidated.

We had a really long thread on this in the past, see: https://www.physicsforums.com/showthread.php?t=729416

EDIT: Also just as an aside, the Sagnac effect is not a local measure of rotation. If it was then it would always agree with the Fermi-Walker definition of rotation but it doesn't as mentioned in post #3. It is a quasi-local measure of rotation since it isn't as global as rotation with respect to spatial infinity but still not entirely local since it requires knowledge of the axial Killing field along the entire closed circuit and on the symmetry axis of the space-time.