Null geodesics in the static Ernst space-time

Abstract

The null geodesics in the equatorial plane of the Ernst space-time have been studied. It is found that they fall essentially into two types depending on the value of the dimensionless magnetic field parameter beta . If beta is less than beta _c=0.094 68 then there exist persisting orbits and stable and unstable circular orbits. However, for beta > beta _c there are no persisting orbits and every particle with non-zero angular momentum must fall into the singularity. For beta > 0 no particle with non-zero angular momentum can escape to infinity. The weak field case beta «1 has been treated in detail and the radii of the stable and unstable circular orbits have been obtained in this limit. Finally, the gravitational redshift has been calculated relative to static observers.