Killing Tensors as Space–Time Metrics

The symmetric Killing tensors of order two associated with orthogonal separable coordinates for the Klein–Gordon equation in flat 2+1-dimensional space-time are considered as metrics. So, as a by-product of variable separation in flat space-time new, generally curved, spaces are generated whose metric again admits Killing tensors. For each coordinate system there are distinguished Killing metrics whose curvature yields an energy-momentum tensor of a matter distribution which is comoving with the underlying separable coordinates. There are simple conformal relations between these particular Killing tensors of the different coordinate systems.