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

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