The Ozsváth–Schücking metric, or the Ozsváth–Schücking solution, is a
vacuum solution of the
Einstein field equations. The metric was published by István Ozsváth and
Engelbert Schücking in 1962.[1] It is noteworthy among vacuum solutions for being the first known solution that is
stationary, globally defined, and singularity-free but nevertheless not isometric to the
Minkowski metric. This stands in contradiction to a claimed strong Mach principle, which would forbid a vacuum solution from being anything but Minkowski without singularities, where the singularities are to be construed as mass as in the
Schwarzschild metric.[2]
It is straightforward to verify that e(0) is timelike, e(1), e(2), e(3) are spacelike, that they are all
orthogonal, and that there are no singularities. The corresponding proper time is
The
Riemann tensor has only one algebraically independent, nonzero component
which shows that the spacetime is
Ricci flat but not
conformally flat. That is sufficient to conclude that it is a vacuum solution distinct from Minkowski spacetime. Under a suitable coordinate transformation, the metric can be rewritten as