A new coordinate condition,and elementary flatness,for axially symmetric interior solutions in general relativity

Two general results for stationary axially symmetric interior solutions of the Einstein or Einstein-Maxwell equations in cylindrical coordinates are derived.Firstly, a coordinate condition for interior solutions is proposed, corresponding to the Weyl coordinate condition used in the exterior.Secondly, it is shown that elementary flatness in the interior is always ensured by realistic boundary conditions and matter tensors, given elementary flatness in the exterior metric.A physical discussion of the results is given, particularly in reference to solutions which have singular struts in them.