Expansion-free electromagnetic solutions of Kerr-Schild class

TR Number
Journal Title
Journal ISSN
Volume Title
AIP Publishing

Starting with the general Kerr_Schild form of the metric tensor,d s2=+l_l (where l is null and _ is flat space_time), a study is made for those solutions of the Einstein_Maxwell equations in which l is geodesic, shear_free, and expansion_free. It is shown that all resulting solutions must be of Petrov type [4] or type [] and the Maxwell field must be null. Because of the expansion_free assumption there exist flat and conformally flat gauge conditions on all metrics in this class; i.e., there exist metrics of this Kerr_Schild form which are flat (or conformally flat) but are not Lorentz_related. A method is given for obtaining meaningful solutions to the field equations with the latter gauge equivalence class removed. A simple example of a radiative field of type [4] along a line singularity exhibits how solutions in this class may be generated.

maxwell equations, tensor methods
Debney, G., "Expansion-free electromagnetic solutions of Kerr-Schild class," J. Math. Phys. 15, 992 (1974); http://dx.doi.org/10.1063/1.1666784