A Former Atheist

[Alex K]

.... and the question what it means to be stationary is really subtle in General Relativity. One can indeed easily go to a spacetime-dependent reference frame in which the earth is fixed at a certain coordinate position while the sun rotates around it. This is allowed in GR because it is set up to be completely coordinate-choice independent by design.

If you make this coordinate change, the transformation of the metric tensor into the geostationary rotating reference frame causes the introduction of large nonvanishing Christoffel connections which introduce "gravitational forces" pulling the entire universe towards the earth such that it rotates around earth once every 24 hours...

Fortunately the chapter of Callaghan's book I consulted is only SR, not GR. I don't know differential geometry or tensor calculus and thus cannot read GR with understanding. I can barely do the SR chapters for that matter, which are written mostly at an introductory calculus level. What baffles me a little is that you can do a rotating reference frame in SR even though SR doesn't allow any problems that involve accelerated motion or gravity. I take that's because the problem was just kinematic, without involving mass or force.

I would recommend Callaghan, though. His writing style is clear, with lengthy explanations to aid in understanding and more steps shown in the math than usual for this kind of book.

You can do a rotating reference frame in SR, but you have to introduce some of the differential geometry machinery of GR in order to pull it off correctly. The difference between SR and GR is then that there is no true spatial curvature and you start out with a minkowskian metric where the line element is simply ds^2 = dt^2 - dx^2 - dy^2 - dz^2. But when you go to a moving frame from there, you have to transform the metric to something more complicated and use riemannian geometry even if it's just SR. Otherwise I wouldn't know how one would correctly take the new coordinates into account.