Abstract
In a space-time admitting a two-parameter Abelian isometry group, and a quadratic Killing tensor with the eigenvalues (λ, λ, μ, μ) and vanishing Lie derivatives with respect to the Killing vectors, we construct a canonical coordinate system. The isometry group acts orthogonally transitively. The Hamilton-Jacobi equation is separable. We give a necessary and sufficient condition for the separability of the Klein-Gordon equation. We obtain Carter's space-times with completely separable Klein-Gordon equation.
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Dietz, W. A characterization of carter's separable space-times. Int J Theor Phys 16, 541–549 (1977). https://doi.org/10.1007/BF01804561
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DOI: https://doi.org/10.1007/BF01804561