Maxwell's equations are covariant under Lorentz transformations. Are they covariant under going to a rotating frame and if not how do they look?
The general covariant Maxwell's equations transform covariantly under general coordinate transformations.
Therefore if we start with Maxwell's equations in Minkowski space in an inertial frame, it is in principle straightforward to work out how the Maxwell's equations become in an accelerated reference frame, e.g. a rotating reference frame. We leave that exercise to the reader.