THE ELECTRIC AND MAGNETIC WEYL TENSORS

The electric and magnetic Weyl tensors, E(ab) and H-ab, are constructed from the Weyl tenser and its dual, respectively, by contracting each twice with an arbitrary time-like unit vector u(a). I consider the invariants E(ab) E(ab) - H-ab H-ab E(ab) H-ab and show that they are independent of the vector u(a) chosen. In spacetimes of Petrov types III and N both these invariants vanish. Two examples are considered, of types N and III, respectively. The properties of E(ab) and H-ab support the view that these spacetimes contain gravitational radiation, and show the close analogy between these tensors and the field vectors of electromagnetism.