Separation of variables and symmetry operators for the conformally invariant Klein-Gordon equation on curved spacetime |
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Authors: | N Kamran R G McLenaghan |
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Institution: | (1) Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada |
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Abstract: | The separability of the conformally invariant Klein-Gordon equation and the Laplace-Beltrami equation are contrasted on two classes of Petrov type D curved spacetimes, showing that neither implies the other. The second-order symmetry operators corresponding to the separation of variables of the conformally invariant Klein-Gordon equation are constructed in both classes and the most general second-order symmetry operator for the conformally invariant Klein-Gordon operator on a general curved background is characterized tensorially in terms of a valence two-symmetric tensor satisfying the conformal Killing tensor equation and further constraints. |
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