  In electromagnetism, the concept of Poynting vector as measured by an
observer is well known. A mathematical analogue in general relativity is the
super-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 of
Weyl-Petrov type I or D, principal observers instantaneously passing through
that point always exist. We survey characterizations of such observers and
study their relation to arbitrary observers. In the non-null electromagnetic
case it is known that, given any observer, there is a principal observer which
moves relative to the first in the direction of his Poynting vector. Replacing
Poynting by super-Poynting yields a possible gravitational analogue; we show
that this analogy indeed holds for any observer when the Petrov type is D, but
only for a one-dimensional variety of observers when the Petrov type is I. We
provide algorithms to obtain the principal observers directly from the electric
and magnetic fields (in the electromagnetic case) or electric and magnetic
parts of the Weyl tensor (in the gravitational case) relative to an arbitrary
observer. It is found that in Petrov type D doubly aligned non-null
Einstein-Maxwell fields (which include all classical charged black hole
solutions) the Poynting and super-Poynting vectors are aligned, at each point
and for each observer, and the principal observers coincide. Our results are
illustrated in simple examples.
