[oddthink]

I've found differential forms to be more useful than GA, but that might just be that I was brought up in the MTW tradition and don't quite get GA.

Whenever I look at GA, I try to figure out where the metric comes in, and I just don't see it.

For context, way back when I did astro theory and wanted to do things like figure out things like the magnetic field structure in the curved spacetime near highly-magnetized rotating conducting spheres, and then do some basic plasma physics in that environment.

The differential geometry approach at least gives the structure to think about that, then you can go down to the index-style notation to actually get the differential equations you need to solve. The GA approach, I'm not even sure how to frame the problem.