Types of electromagnetic fields around black holes in Schwarzschild, Kerr and Kerr-Newmann spacetimes

We consider electromagnetic fields having an angular momentum density in a locally non-rotating reference frame in Schwarzschild, Kerr, and Kerr-Newman spacetimes. The state of motion of such fields is assessed with two families of observers, the locally non-rotating ones and those of vanishing Poynting vector comoving with the fields. The velocity fields of the electromagnetic fields in the locally non-rotating reference frames are determined using the 3+1 decomposition formalism. The motion of the electromagnetic fields is also presented for the two observer families considering the effects due to both rotation of the fields and the dragging of reference frames. From a methodological point of view, and considering a classification of the electromagnetic field based on its invariants, it is convenient to separate the consideration of the vanishing-Poynting observers into two cases corresponding to the pure and non-pure fields, additionally if there are regions where the field rotates with the speed of light (light surfaces) it becomes necessary to split these observers into two subfamilies. We present several examples of relevance in astrophysics and general relativity, such as pure rotating dipolar-like magnetic fields and the electromagnetic field of the Kerr-Newman solution. For the latter example, using Carter observers, we find that the electromagnetic energy is comoving with the gravitational super-energy, which confirms and extends results reported by other authors.