Electromagnetic fields in the Godel universe

Abstract

Perturbative electromagnetic fields are investigated in the Godel universe using the Debye potential (two-component Hertz potential) formalism. The Godel space-time lends itself to this approach since it is algebraically special (Petrov D). With the usual system of coordinates used in the text describing the Godel universe, the three of the basis coordinate vectors delta / delta x0, delta / delta x1 and delta / delta x3 which are Killing, the field at infinity in these directions remains oscillatory, while for the remaining non-Killing coordinate x2 the field decays at both extremities. The result compares dramatically well with the behaviour of the null geodesics in the Godel universe.