- #31

pmb

Switching into a rotating frame changes the geometry of space. The rotating observer will see the universe differently than the nonrotating observer because in his frame, space-time has a different geometry. Space-time, in both pictures, has zero curvature, but the geometry is different, thus switching frames will introduce a "space-time distortion".

I assumed that Carter was asking about curvature.

And I wonder about the rest of what you say. To me the "geometry" is an intrinsic property of a manifold once a metric is attached to it. When you change frames all you're really doing is chaning the coordinate system. You're not chaning the geometry of spacetime itself. The metric is a geometric object and when you change coordinates wha you're doing is merely changing the components - not altering the geometric entity itself. E.g. Think of the analogy with vectors since they too are geometric objects like the metric. If you have a Cartesian vector and you change coordinates then you change the components of the vector but you don't change the geometric object itself.

Pmb