Heinz Pagels

ELECTROMAGNETIC PLANE WAVE SOLUTIONS IN GENERAL RELATIVITY

Abstract The problem of Rainich for null fields is examined, and it is found that for particular geometries the electromagnetic field is not unique. In the special case where the propagation and polarization vectors are harmonic, the geometry admits an electromagnetic potential which excludes the existence of magnetic monopoles. An explicit solution for a null electromagnetic plane wave of arbitrary pulse shape is obtained. It is found that there is generated no gravitational field external to the pulse.

Divergence Conditions and the Gravitational Field Equations

It is shown that in addition to the four divergence laws Tαβ|β = 0, stress tensors satisfying the Einstein field equations must also satisfy the additional divergence conditions (Tγα|β−Tγβ|α)|γ=0. Conversely, under quite general assumptions these ten conditions on the source, Tαβ, dictate the metric—matter connection proposed by Einstein.