Vanishing Poynting Observers and Electromagnetic Field Classification in Kerr and Kerr-Newman Spacetimes

We consider electromagnetic fields having an angular momentum density in a locally nonrotating reference frame in Schwarzschild, Kerr, and Kerr-Newman spacetimes. The nature of such fields is assessed with two families of observers, the locally nonrotating ones and those of vanishing Poynting flux. The velocity fields of the vanishing-Poynting observers in the locally nonrotating reference frames are determined using the 3 + 1 decomposition formalism. 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 nonpure 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, we see that vanishing-Poynting observers also measure a vanishing super-Poynting vector, confirming recent results in the literature. Finally, for all nonnull electromagnetic fields, we present the 4-velocity fields of vanishing Poynting observers in an arbitrary spacetime.