Index gymnastics of electromagnetism quantities

[coleman123]

This bothers me, and the question is simple:

If am working with a non-minkowski metric g, when raising or lowering indexes of electromagnetism quantities, for example the electromagnetic tensor F, or the vector potential A, should I use my curved spacetime metric g or the minkowski metric n?

 

[bcrowell]

The actual metric. The Minkowski metric is at best an approximation to the curved-spacetime metric.

 

[coleman123]

Thanks!

 

[WannabeNewton]

If am working with a non-minkowski metric g, when raising or lowering indexes of electromagnetism quantities, for example the electromagnetic tensor F, or the vector potential A, should I use my curved spacetime metric g or the minkowski metric n?

Coordinate indices are raised and lowered with $g$ but tetrad indices are raised and lowered using $\eta$, be it curved space-time or flat space-time.