Bivector Formalism in General Relativity

Abstract

The use of bivectors, or skew symmetric tensors, is a powerful research tool in general relativity. Such objects arise naturally in the context of electromagnetism. We therefore introduce them via electromagnetic test fields on arbitrary space-times. All details are provided including an important application to electromagnetic radiation due to Ivor Robinson. This is followed by the extension of bivector theory to gravitational fields. An explicit illustration of their use in relation to Kerr space-time is given.