# Is B always the curl of A in curved space time?

• A
yourWitten
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 if not, how it should be modified.

I know this question is extremely simple but I'm still developing intuition on GR.

Staff Emeritus