Classification of homogeneous Stäckel spacetimes (Q1886184)

The authors present an approach to the classification of spatially homogeneous space-times, where the geodesic equations in the Hamilton-Jacobi form can be integrated by the method of complete separation of variables; such spaces are called Stäckel space-times. A necessary and sufficient condition for a space-time to be Stäckel is the existence of a complete set of Killing vector and tensor fields. In this paper the authors classify spatially homogeneous Stäckel space-times with a so-called type \((2,1)\) complete set by providing a list of all solutions in form of a metric tensor.