Killing tensors as space-time metrics (Q1279757)

Symmetric Killing tensors of order two associated with the separation of the Klein-Gordon equation are considered as metrics. Next from the Stäckel system of any considered coordinate system an \(n-1\)-parameter family of metrics is generated. These Killing metrics taken from the associated Stäckel system generate massive solutions of the Einstein equations with the source of curvature at rest with respect to the coordinates. The conformal relationships between the conformally flat Killing metrics and the original flat ones are also described.