On a construction of quasi-Einstein shearfree spacetimes

Abstract

In this article we prove that a certain class of smooth Sasakian manifolds admits lifts to 4-dimensional quasi-Einstein shearfree spacetimes of Petrov type II or D. This is related to an analogous result by Hill, Lewandowski and Nurowski [4] for general real-analytic CR manifolds. In particular, this holds for all tubular CR manifolds. Furthermore, we show that any Sasakian manifold with underlying Khler-Einstein manifold with non-zero Einstein constant has a lift to a shearfree Einstein metric of Petrov type II or D.