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SomeMichGuy · M
In a curved spacetime, the notion of being able to maintain a direction is slightly more challenging than in a non-curved spacetime.
The "affine connection" allows for the parallel transport of vectors through a curved spacetime, so that one *can* compare vectors at different points along a curved spacetime. What a concept!
For more on this, you can see a very reader-friendly text, [i]Gravitation,[/i] by Charles W. Misner, Kip S. Thorne, and the late John A. Wheeler.
The "affine connection" allows for the parallel transport of vectors through a curved spacetime, so that one *can* compare vectors at different points along a curved spacetime. What a concept!
For more on this, you can see a very reader-friendly text, [i]Gravitation,[/i] by Charles W. Misner, Kip S. Thorne, and the late John A. Wheeler.