@Orodruin I am familiar with the covariant expressions of Maxwell's equations but having trouble working this out. In particular http://sedici.unlp.edu.ar/bitstream/handle/10915/125010/Documento_completo.pdf-PDFA.pdf?sequence=1 Eq. 2.24 suggests that the formula remains the same, but I don't see...
By definition of the vector potential we may write
\nabla \times A =B
at least in flat space. Does this relation hold in curved space? I am particularly interested if we can still write this in a spatially flat Friedmann-Robertson-Walker background with metric ds^2=dt^2-a^2(dx^2+dy^2+dz^2) and...