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.

 

[sardar]

As a scientist, it is important to use the appropriate metric for the specific situation at hand. In the case of electromagnetism quantities, it is necessary to use the metric that is consistent with the geometry of the system being studied. If you are working with a non-Minkowski metric, then it is appropriate to use that metric when raising or lowering indices for the electromagnetic tensor F and the vector potential A. This is because the curvature of spacetime affects the behavior of electromagnetic fields, and using the incorrect metric could lead to incorrect results. Therefore, it is crucial to carefully consider the geometry of the system and use the appropriate metric for accurate analysis.