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Oct15-11, 12:08 PM
P: 1,115
Quote Quote by DaleSpam View Post
If the sphere is rigid then it is not distorted by definition. There may be tidal forces acting on it, but since it is rigid that doesn't affect its shape. Particularly not if you are interested only in covariant measures from the metric and not in coordinate-dependent measures.

An elastic object will get "squeezed" into an ellipsoidal shape as it falls towards the shell. As it nears the shell the squeezing will reach the maximum. As it falls through the shell it will unsqueeze until as it reaches the interior of the shell it is completely unsqueezed. The proper time between ticks will remain unchanged throughout the fall, and the proper diameter inside the shell will be the same as the proper diameter at infinity.
See my remarks to Sam Gralla on that issue in #14.
I think what you are really interested in is one continuous coordinate system that covers the whole spacetime.
Not really. Just an accurate prediction of what the observer measures, and how obtained. Whatever combo of coordinate systems is used is up to whoever tackles it.
The distant measures you mention will depend on your choice of coordinates.
Please elaborate. Just like the twin cycle clock method I outlined elsewhere, one can use differential comparison techniques to eliminate various 'ambiguities'.