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In electromagnetism, the concept of Poynting vector as measured by anobserver is well known. A mathematical analogue in general relativity is thesuper-Poynting vector of the Weyl tensor. Observers for which the(super-)Poynting vector vanishes are called principal. When, at a given point,the electromagnetic field is non-null, or the gravitational field is ofWeyl-Petrov type I or D, principal observers instantaneously passing throughthat point always exist. We survey characterizations of such observers andstudy their relation to arbitrary observers. In the non-null electromagneticcase it is known that, given any observer, there is a principal observer whichmoves relative to the first in the direction of his Poynting vector. ReplacingPoynting by super-Poynting yields a possible gravitational analogue; we showthat this analogy indeed holds for any observer when the Petrov type is D, butonly for a one-dimensional variety of observers when the Petrov type is I. Weprovide algorithms to obtain the principal observers directly from the electricand magnetic fields (in the electromagnetic case) or electric and magneticparts of the Weyl tensor (in the gravitational case) relative to an arbitraryobserver. It is found that in Petrov type D doubly aligned non-nullEinstein-Maxwell fields (which include all classical charged black holesolutions) the Poynting and super-Poynting vectors are aligned, at each pointand for each observer, and the principal observers coincide. Our results areillustrated in simple examples.

Poynting vector, super-Poynting vector, and principal observers in electromagnetism and general relativity