Killing metrics in two dimension

In two examples of the 10 orthogonal coordinate systems in 1+1 - dimensional flat spacetime allowing for a separation of the Klein-Gordon equation the associated symmetric Killing tensor fields of order 2 are considered as new metrics replacing the original flat ones. In the arising curved spaces the horizons of the separable coordinate domains become horizons of true curvature singularities; in simple cases a physical interpretation in the framework of 2-dimensional gravity is possible. (author)