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We study a non-uniformly rotating universe outside a Schwarzschild black holeby generating a time-dependent manifold of revolution around a straight line.In this simple model where layers of spherical shells of the universenon-uniformly rotate, the Einstein field equations require this phenomenon tobe caused by a static mass-energy distribution with time-dependent$T^{\phi\phi}$ (quadratic with time) and $T^{r\phi}=T^{\phi r}$ (linear withtime). This indicates that a time-dependent stress along a certain directionresults in a spacetime shift in that direction. For this model however, suchmaterial violates the null energy condition. Incidentally, the variouscoordinate systems describing the Schwarzschild solution can be viewed asarising from the freedom in parametrising the straight line and the radialfunction in the general method of constructing spacetime by generatingmanifolds of revolution around a given curve.

A rotating universe outside a Schwarzschild black hole where spacetime itself non-uniformly rotates