Characteristic surfaces and characteristic initial data for the generalized Einstein–Maxwell field equations

The characteristic hypersurfaces of the source-free generalized Einstein–Maxwell field equations are investigated. It is shown that such hypersurfaces can be null, and it appears as though they may also be spacelike or timelike. Examples of characteristic initial data on spacelike and timelike hypersurfaces are presented, and it turns out that these examples involve very intense gravitational and electromagnetic fields when the coupling constant k is small in magnitude.