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.
@Riemann Not on my phone, no... I may have a look on my external hard drive later today or over the next few days.
I have something to do today that may take a lot out of me again - and I'm still recovering from walking out on Soon to be ex the other day, too. Oh... and a work event for soon to be ex tomorrow, too. I have to attend as well because I will be working as his carer. His employer needs to learn about his needs and how to spot visual cues in him before I can trust him to go alone.
After the major blow up the other day and the fact that I know that the other guy that he blew up at is going to be there, too... it'll take a while to get to that stage though.
