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A.T.
A.T. is offline
#5
Mar23-08, 10:50 AM
P: 3,537
Quote Quote by siphon View Post
If we use this gravity profile to explain a GR space-time well, in the fabric of space-time, is there a peak in the center of the well? The center point has the same gravity number as distant space so should it have the same space-time fabric height? It would look like a mountain in a hole, with the peak height the same as distant space.
No. you misunderstand how gravity is modeled in GR. There is no "space-time fabric height". The distortion of space-time has an maximum in the center of a sphere, causing a maximal time dilation there. Free fallers are always drawn towards areas of higher time dilatation. But at a point of locally maximal time dilatation, there is nowhere else to go.

Try this visualization:
http://www.adamtoons.de/physics/gravitation.swf
If you set "initial position" to zero, the free falling object is placed at the center of the sphere. And it stays there because it's geodesic world line doesn't deviate in any space direction. The object moves only trough time by moving straight ahead trough space-time.