Some notes on stationary vacuum solutions of the Einstein equations with shearing nongeodesic eigenrays

The stationary vacuum solutions of the Einstein equations of General Relativity give the external space-time around stationary mass distributions, as e.g. final states of stellar evolution. The Kerr solution has shear-free geodesic eigenrays and describes all black hole configurations with good asymptotic behaviour at infinity. Other solutions of this class are unphysical. Classes with shearing geodesic or shearfree nongeodesic eigenrays do not contain physical solutions at all, so for other physical configurations one must turn to the generic case of shearing nongeodesic eigenrays. For the stationary axisymmetric case Ansätze for solutions can be formulated in form of a specific functional dependence between the parameters of shear and nongeodesicity, unless they both are constants. Here we investigate the second subcase. Our result is that there is no solution of the vacuum Einstein equations in this subclass, except when both parameters vanish.