I am thinking about this: A vacuum solution means vanishing Ricci tensor. The Ricci tensor is a contraction of the Riemann, which itself involves contains second derivatives of the metric. Thus they are different Lorentzian metrics with vanishing Ricci tensor. But is there ultimately one metric which has all other vacuum solutions as a special case? Like Kerr has Schwarzschild has Minkowski, by setting the free parameters correctly. Furthermore, how many free parameters can a metric in the vacuum have?
I hope this make sense.
Edit: I guess I am not sure if I am thinking about it in the right way. The most general solution of the vacuum Eq. is a metric with 10 degrees of freedom. By, for example, fixing 9 of them to certain values, we obtain a metric like Schwarzschild, modeling the exterior of a spherical object. Fixing 8 of them in a certain way gives a metric which models the exterior of central, spinning object. Is there now, theoretically, a way to fix some of those freedoms to model every other possible vacuum scenario imaginable? Like binaries etc.
Still not sure whether my question actually makes sense.